11-8 Solving Integer Equations

Warm UpUse mental math to find each solution.

1. 6 + x = 12 2. 3x = 15

3. = 4 4. x – 8 = 12

x = 6 x = 5

x = 20 x = 20x 5__

11-8 Solving Integer Equations

Problem of the Day

Marie spent $15 at the fruit stand, buying peaches that cost $2 per container and strawberries that cost $3 per container. She bought the same number of containers of each fruit. How many containers each of peaches and strawberries did she buy?

3

11-8 Solving Integer Equations

Preview of MA.7.A.3.3 Formulate and use different strategies to solve one-step…linear equations.

Also Preview of MA.7.A.3.2

Sunshine State Standards

11-8 Solving Integer Equations

Vocabulary

Identity Property

11-8 Solving Integer Equations

Solve –8 + y = –13. Check your answer.

–8 + y = –13 y is added to –8.

+ 8 + 8 Add 8 to both sides.

y = –5

Check

–8 + y = –13 Write the equation.

Substitute –5 for y.

–5 is a solution.

–8 + (–5) = –13 ?

–13 = –13 ?

Additional Example 1A: Adding and Subtracting to Solve Equations

11-8 Solving Integer Equations

Subtracting a number is the same as adding its opposite. To solve the equation on the previous slide using algebra tiles, you can add eight yellow tiles to both sides and then remove zero pairs.

Helpful Hint

11-8 Solving Integer Equations

Additional Example 1B: Adding and Subtracting to Solve Equations

Solve n – 2 = –8. Check your answer.

n – 2 = –8 2 is subtracted from n.

+ 2 + 2 Add 2 to both sides to undo the subtraction.

n = –6

Check

n – 2 = –8 Write the equation.

Substitute –6 for n.

–6 is a solution.

–6 – 2 = –8 ?

–8 = –8 ?

11-8 Solving Integer Equations

Check It Out: Example 1A

Solve –2 + y = –7. Check your answer.

–2 + y = –7 y is added to –2.

+ 2 + 2 Add 2 to both sides.

y = –5

Check

–2 + y = –7 Write the equation.

Substitute –5 for y.

–5 is a solution.

–2 + (–5) = –7 ?

-7 = -7 ?

11-8 Solving Integer Equations

Check It Out: Example 1B

Solve n – 6 = –14. Check your answer.

n – 6 = –14 6 is subtracted from n.

+ 6 + 6 Add 6 to both sides to undo the subtraction.

n = –8

Check

n – 6 = –14 Write the equation.

Substitute –8 for n.

–8 is a solution.

–8 – 6 = –14 ?

–14= –14 ?

11-8 Solving Integer Equations

Additional Example 2A: Multiplying and Dividing to Solve Equations

Solve 4m = –20. Check your answer.

=m is multiplied by 4. Divide both sides by 4 to undo the multiplication.

m = –5

Check

4m = –20 Write the equation.

Substitute –5 for m.

–5 is a solution.

4(–5) = –20 ?

–20 = –20 ?

4m 4 ___ -20

4 ___

11-8 Solving Integer Equations

3 • = 3 • (–7) x is divided by 3. Multiply both sides by 3 to undo the division.

x = –21

Check

= –7 Write the equation.

Substitute –21 for x.

–21 is a solution.

–21 ÷ 3 = –7 ?

–7 = –7 ?

x 3 __

x 3 __

Additional Example 2B: Multiplying and Dividing to Solve Equations

Solve = –7. Check your answer. x 3

11-8 Solving Integer Equations

Check It Out: Example 2A

Solve 3n = –15. Check your answer.

=n is multiplied by 3. Divide both sides by 3 to undo the multiplication.

n = –5

Check

3n = –15 Write the equation.

Substitute –5 for n.

–5 is a solution.

3(–5) = –15?

–15 = –15 ?

3n 3 ___ –15

3 ___

11-8 Solving Integer Equations

Check It Out: Example 2B

Solve = –6. Check your answer.

4 • = 4 • (–6) y is divided by 4. Multiply both sides by 4 to undo the division.

y = –24

Check

Write the equation.

Substitute –24 for y.

–24 is a solution.

–24 ÷ 4 = –6 ?

–6 = –6 ?

y 4 __

y 4 __

= –6 y 4 __