1.5 – solving inequalities. *just like solving equations*
TRANSCRIPT
1.5 – Solving Inequalities
1.5 – Solving Inequalities
*Just like solving equations*
1.5 – Solving Inequalities
*Just like solving equations*
Example 1
1.5 – Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
1.5 – Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
7x – 5 > 6x – 4
1.5 – Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
7x – 5 > 6x – 4
-6x -6x
1.5 – Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
7x – 5 > 6x – 4
-6x -6x
x – 5
1.5 – Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
7x – 5 > 6x – 4
-6x -6x
x – 5 > -4
1.5 – Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
7x – 5 > 6x – 4
-6x -6x
x – 5 > -4
+5 +5
1.5 – Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
7x – 5 > 6x – 4
-6x -6x
x – 5 > -4
+5 +5
x
1.5 – Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
7x – 5 > 6x – 4
-6x -6x
x – 5 > -4
+5 +5
x >
1.5 – Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
7x – 5 > 6x – 4
-6x -6x
x – 5 > -4
+5 +5
x > 1
1.5 – Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
7x – 5 > 6x – 4
-6x -6x
x – 5 > -4
+5 +5
x > 1
1.5– Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
7x – 5 > 6x – 4
-6x -6x
x – 5 > -4
+5 +5
x > 1
0
1.5– Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
7x – 5 > 6x – 4
-6x -6x
x – 5 > -4
+5 +5
x > 1
0 1
1.5– Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
7x – 5 > 6x – 4
-6x -6x
x – 5 > -4
+5 +5
x > 1
0 1
1.5– Solving Inequalities
*Just like solving equations*
Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.
7x – 5 > 6x – 4
-6x -6x
x – 5 > -4
+5 +5
x > 1
0 1
Example 2
Example 2 – Solve –m < -m + 4 and graph. 9
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
–9m
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
–9m <
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
–9m < -m + 4
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
–9m < -m + 4 +m +m
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
–9m < -m + 4 +m +m –8m
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
–9m < -m + 4 +m +m –8m <
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
–9m < -m + 4 +m +m –8m < 4
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
–9m < -m + 4 +m +m –8m < 4
-8 -8
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
–9m < -m + 4 +m +m –8m < 4
-8 -8 m
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
–9m < -m + 4 +m +m –8m < 4
-8 -8 m >
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 9
9·–m < -m + 4 ·9 9
–9m < -m + 4 +m +m –8m < 4
-8 -8 m >
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 99·–m < -m + 4 ·9 9–9m < -m + 4 +m +m –8m < 4
-8 -8 m > -½
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 99·–m < -m + 4 ·9 9–9m < -m + 4 +m +m –8m < 4
-8 -8 m > -½
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 99·–m < -m + 4 ·9 9–9m < -m + 4 +m +m –8m < 4
-8 -8 m > -½
0
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 99·–m < -m + 4 ·9 9–9m < -m + 4 +m +m –8m < 4
-8 -8 m > -½
0-1½ -1 -½
Example 2 – Solve –m < -m + 4 and graph. 9
–m < -m + 4 99·–m < -m + 4 ·9 9–9m < -m + 4 +m +m –8m < 4
-8 -8 m > -½
0-1½ -1 -½
Example 3
Example 3 – Define a variable and write an inequality for each problem. Then solve.
Example 3 – Define a variable and write an inequality for each problem. Then solve.
The product of –4 and a number is at least 35.
Example 3 – Define a variable and write an inequality for each problem. Then solve.
The product of –4 and a number is at least 35.
Example 3 – Define a variable and write an inequality for each problem. Then solve.
The product of –4 and a number is at least 35.
-4x
Example 3 – Define a variable and write an inequality for each problem. Then solve.
The product of –4 and a number is at least 35.
-4x
Example 3 – Define a variable and write an inequality for each problem. Then solve.
The product of –4 and a number is at least 35.
-4x >
Example 3 – Define a variable and write an inequality for each problem. Then solve.
The product of –4 and a number is at least 35.
-4x >
Example 3 – Define a variable and write an inequality for each problem. Then solve.
The product of –4 and a number is at least 35.
-4x >
Example 3 – Define a variable and write an inequality for each problem. Then solve.
The product of –4 and a number is at least 35.
-4x > 35
Example 3 – Define a variable and write an inequality for each problem. Then solve.
The product of –4 and a number is at least 35.
-4x > 35
-4 -4
Example 3 – Define a variable and write an inequality for each problem. Then solve.
The product of –4 and a number is at least 35.
-4x > 35
-4 -4
x <
Example 3 – Define a variable and write an inequality for each problem. Then solve.
The product of –4 and a number is at least 35.
-4x > 35
-4 -4
x < -8.75
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%( )
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%( )
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%( ? )
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%( ? )
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%( ? ) +
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%( ? ) +
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%( ? ) + 25%( )
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%( ? ) + 25%( )
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%( ? ) + 25%( ? )
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%( ? ) + 25%( ? )
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%( ? )
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%( ? )
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x)
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x)
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 80
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 80
0.75
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 80
0.75(76)
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 80
0.75(76) +
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 80
0.75(76) + 0.25
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 80
0.75(76) + 0.25(x)
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 80
0.75(76) + 0.25(x) ≥ 80
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 80
0.75(76) + 0.25(x) ≥ 80
57
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 80
0.75(76) + 0.25(x) ≥ 80
57 + 0.25x
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 800.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 800.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80
-57 -57
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 80
0.75(76) + 0.25(x) ≥ 80
57 + 0.25x ≥ 80
-57 -57
0.25x
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 80
0.75(76) + 0.25(x) ≥ 80
57 + 0.25x ≥ 80
-57 -57
0.25x ≥ 23
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 800.75(76) + 0.25(x) ≥ 8057 + 0.25x ≥ 80
-57 -57 0.25x ≥ 23 0.25 0.25
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 800.75(76) + 0.25(x) ≥ 8057 + 0.25x ≥ 80
-57 -57 0.25x ≥ 23 0.25 0.25
x
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 800.75(76) + 0.25(x) ≥ 8057 + 0.25x ≥ 80
-57 -57 0.25x ≥ 23 0.25 0.25
x ≥
Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?
75%(76) + 25%(x) ≥ 800.75(76) + 0.25(x) ≥ 8057 + 0.25x ≥ 80
-57 -57 0.25x ≥ 23 0.25 0.25
x ≥ 92