1.6 – solving compound and absolute value inequalities
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1.6 – Solving Compound and Absolute Value Inequalities
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17
-7 -7
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17
-7 -7
6
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17
-7 -7
6 <
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17
-7 -7
6 < 2x
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17
-7 -7
6 < 2x
2 2
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2 2 3
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2 2 3 <
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2 2 3 < x
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2 2 3 < x
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x 2 2 3 < x
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x < 2 2 3 < x
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x < 10 2 2 3 < x
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x <
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x < 5
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x < 5
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x < 5
3 < x
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5
3 < x
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5
3 < x < 5
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5
3 < x ≤ 5
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5
3 < x ≤ 5
0 3 5
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5
3 < x ≤ 5
0 3 5
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5
3 < x ≤ 5
0 3 5
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5
3 < x ≤ 5
0 3 5
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5
3 < x ≤ 5
0 3 5
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > -3 or y + 4 ≤ -3
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > -3 or y + 4 ≤ -3
+2 +2 -4 -4
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > -3 or y + 4 ≤ -3
+2 +2 -4 -4
y > -1 or y ≤ -7
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > -3 or y + 4 ≤ -3
+2 +2 -4 -4
y > -1 or y ≤ -7
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > -3 or y + 4 ≤ -3
+2 +2 -4 -4
y > -1 or y ≤ -7
-7 -1 0
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > -3 or y + 4 ≤ -3
+2 +2 -4 -4
y > -1 or y ≤ -7
-7 -1 0
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > -3 or y + 4 ≤ -3
+2 +2 -4 -4
y > -1 or y ≤ -7
-7 -1 0
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > -3 or y + 4 ≤ -3
+2 +2 -4 -4
y > -1 or y ≤ -7
-7 -1 0
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > -3 or y + 4 ≤ -3
+2 +2 -4 -4
y > -1 or y ≤ -7
-7 -1 0
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > -3 or y + 4 ≤ -3
+2 +2 -4 -4
y > -1 or y ≤ -7
-7 -1 0
Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4
Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4
a < 4 or a > -4
Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4
a < 4 or a > -4
-4 0 4
Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4
a < 4 or a > -4
(b) Solve |a| > 4. Graph the solution on a number line.
-4 0 4
Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4
a < 4 or a > -4
(b) Solve |a| > 4. Graph the solution on a number line.
|a| > 4
-4 0 4
Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4
a < 4 or a > -4
(b) Solve |a| > 4. Graph the solution on a number line.
|a| > 4
a > 4 or a < -4
-4 0 4
Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4
a < 4 or a > -4
(b) Solve |a| > 4. Graph the solution on a number line.
|a| > 4
a > 4 or a < -4
-4 0 4
-4 0 4
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ 6
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ 6 3x – 12 < -6
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ 6 3x – 12 < -6
+12 +12 _ +12 +12
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ 6 3x – 12 < -6
+12 +12 _ +12 +12
3x ≥ 18 3x < 6
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ 6 3x – 12 < -6
+12 +12 _ +12 +12
3x ≥ 18 3x < 6
3 3 3 3
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ 6 3x – 12 < -6
+12 +12 _ +12 +12
3x ≥ 18 3x < 6
3 3 3 3
x ≥ 6 x < 2
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ 6 3x – 12 < -6
+12 +12 _ +12 +12
3x ≥ 18 3x < 6
3 3 3 3
x ≥ 6 x < 2
0 2 6