student learning goal chart
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Student Learning Goal Chart. Chapter 10. Pre-Algebra Learning Goal Students will understand solving linear equations and inequalities. Students will understand solving linear equations and inequalities by being able to do the following:. Learn to solve two-step equations (10.1). - PowerPoint PPT PresentationTRANSCRIPT
Student Learning Goal Chart
Chapter 10
Pre-Algebra Learning Goal
Students will understand solving linear equations and inequalities.
Students will understand solving linear equations and inequalities by being able to do the following:
• Learn to solve two-step equations (10.1)
Pre-Algebra
10-1 Solving Two-Step Equations
Today’s Learning Goal Assignment
Learn to solve two-step equations.
Pre-Algebra
10-1 Solving Two-Step Equations
Pre-Algebra HW
Page 500#15-32
Pre-Algebra
10-1 Solving Two-Step Equations10-1 Solving Two-Step Equations
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
10-1 Solving Two-Step Equations
Warm UpSolve.
1. x + 12 = 35
2. 8x = 120
3. = 7
4. –34 = y + 56
x = 23
x = 15
y = 63
Pre-Algebra
10-1 Solving Two-Step Equations
y = –90
y9
Pre-Algebra
10-1 Solving Two-Step Equations
Problem of the Day
x is an odd integer. If you triple x and then subtract 7, you get a prime number. What is x? (Hint: Think about what the prime number must be in order for x to be an odd.)
x = 3
Pre-Algebra
10-1 Solving Two-Step Equations
Today’s Learning Goal Assignment
Learn to solve two-step equations.
Pre-Algebra
10-1 Solving Two-Step Equations
Sometimes more than one inverse operation is needed to solve an equation. Before solving, ask yourself, “What is being done to the variable, and in what order?” Then work backward to undo the operations.
Pre-Algebra
10-1 Solving Two-Step Equations
The mechanic’s bill to repair Mr. Wong’s car was $650. The mechanic charges $45 an hour for labor, and the parts that were used cost $443. How many hours did the mechanic work on the car?
Additional Example 1: Problem Solving Application
Pre-Algebra
10-1 Solving Two-Step Equations
Additional Example 1 Continued
11 Understand the Problem
The answer is the number of hours the mechanic worked on the car.
List the important information:
Let h represent the hours the mechanic worked.
• The parts cost $443.• The labor cost $45 per hour.• The total bill was $650.
Total bill = Parts + Labor
650 = 443 + 45h
Pre-Algebra
10-1 Solving Two-Step Equations
Think: First the variable is multiplied by 45, and then 443 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 443 from both sides of the equation, and then divide both sides of the new equation by 45.
22 Make a Plan
Additional Example 1 Continued
Pre-Algebra
10-1 Solving Two-Step Equations
650 = 443 + 45h
Solve33
–443 –443 Subtract to undo the addition.
207 = 45h
4.6 = h
The mechanic worked for 4.6 hours on Mr. Wong’s car.
Additional Example 1 Continued
Divide to undo multiplication.207 45h45 45=
Pre-Algebra
10-1 Solving Two-Step Equations
If the mechanic worked 4.6 hours, the labor would be $45(4.6) = $207. The sum of the parts and the labor would be $443 + $207 = $650.
Look Back44
Additional Example 1 Continued
Pre-Algebra
10-1 Solving Two-Step Equations
The mechanic’s bill to repair your car was $850. The mechanic charges $35 an hour for labor, and the parts that were used cost $275. How many hours did the mechanic work on your car?
Try This: Example 1
Pre-Algebra
10-1 Solving Two-Step Equations
Try This: Example 1 Continued
11 Understand the Problem
The answer is the number of hours the mechanic worked on your car.
List the important information:
Let h represent the hours the mechanic worked.
• The parts cost $275.
• The labor cost $35 per hour.
• The total bill was $850.
Total bill = Parts + Labor
850 = 275 + 35h
Pre-Algebra
10-1 Solving Two-Step Equations
Think: First the variable is multiplied by 35, and then 275 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 275 from both sides of the equation, and then divide both sides of the new equation by 35.
22 Make a Plan
Try This: Example 1 Continued
Pre-Algebra
10-1 Solving Two-Step Equations
850 = 275 + 35h
Solve33
–275 –275 Subtract to undo the addition.
575 = 35h
16.4 h
The mechanic worked for about 16.4 hours on your car.
Try This: Example 1 Continued
Divide to undo multiplication.575 35h35 35=
Pre-Algebra
10-1 Solving Two-Step Equations
If the mechanic worked 16.4 hours, the labor would be $35(16.4) = $574. The sum of the parts and the labor would be $275 + $574 = $849.
Look Back44
Try This: Example 1 Continued
Pre-Algebra
10-1 Solving Two-Step Equations
Additional Example 2A: Solving Two-Step Equations
A. + 7 = 22
Solve.
Think: First the variable is divided by 3, and then 7 is added. To isolate the variable, subtract 7, and then multiply by 3.
– 7 – 7 Subtract to undo addition.
n3
+ 7 = 22n3
Multiply to undo division.3 = 3 15n3n = 45
n3
= 15
Pre-Algebra
10-1 Solving Two-Step Equations
Additional Example 2A Continued
Substitute 45 into the original equation.
Check + 7 = 22n3
? + 7 = 2245
315 + 7 = 22
?
Pre-Algebra
10-1 Solving Two-Step Equations
Additional Example 2B: Solving Two-Step Equations
B. 2.7 = –1.3m + 6.6
Think: First the variable is multiplied by –1.3, and then 6.6 is added. To isolate the variable, subtract 6.6, and then divide by –1.3.
2.7 = –1.3m + 6.6–6.6 –6.6 Subtract to undo addition.–3.9 = –1.3m
Divide to undo multiplication.
3 = m
–1.3 –1.3–3.9 = –1.3m
Pre-Algebra
10-1 Solving Two-Step Equations
Additional Example 2C: Solving Two-Step Equations
C. = 9y – 4 3
Think: First 4 is subtracted from the variable, and then the result is divided by 3. To isolate the variable, multiply by 3, and then add 4.
= 9y – 43
y – 4 = 27 + 4 + 4 Add to undo subtraction.
y = 31
3 · 3 · Multiply to undo division.= 9y – 43
Pre-Algebra
10-1 Solving Two-Step Equations
Try This: Example 2A
A. + 5 = 29
Solve.
Think: First the variable is divided by 4, and then 5 is added. To isolate the variable, subtract 5, and then multiply by 4.
– 5 – 5 Subtract to undo addition.
n4
+ 5 = 29n4
Multiply to undo division.4 = 4 24n4
n = 96
Pre-Algebra
10-1 Solving Two-Step Equations
Substitute 96 into the original equation.
Check + 5 = 29n4
? + 5 = 2996
424 + 5 = 29
?
Try This: Example 2A Continued
Pre-Algebra
10-1 Solving Two-Step Equations
Try This: Example 2B
B. 4.8 = –2.3m + 0.2
Think: First the variable is multiplied by –2.3, and then 0.2 is added. To isolate the variable, subtract 0.2, and then divide by –2.3.
4.8 = –2.3m + 0.2–0.2 –0.2 Subtract to undo addition.4.6 = –2.3m
Divide to undo multiplication.
–2 = m
–2.3 –2.3 4.6 = –2.3m
Pre-Algebra
10-1 Solving Two-Step Equations
Try This: Example 2C
C. = 8y – 2 4
Think: First 2 is subtracted from the variable, and then the result is divided by 4. To isolate the variable, multiply by 4, and then add 2.
= 8y – 24
y – 2 = 32 + 2 + 2 Add to undo subtraction.
y = 34
4 · 4 · Multiply to undo division.= 8y – 24
Pre-Algebra
10-1 Solving Two-Step Equations
Solve.
1. – 3 = 10
2. 7y + 25 = –24
3. –8.3 = –3.5x + 13.4
4. = 3
5. The cost for a new cell phone plan is $39 per month plus a one-time start-up fee of $78. If you are charged $1014, how many months will the contract last?
Lesson Quiz
y = –7
x = –117
x = 6.2
y = 28
24 months
x–9
y + 5 11