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11-8 Solving Integer Equations
Warm Up
Use mental math to find each solution.
1. 6 + x = 12 x = 6
2. 3x = 15
x
3. __
=
4
5
4. x – 8 = 12 x = 20
x = 20
x=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
Sunshine State Standards
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
11-8 Solving Integer Equations
Vocabulary
Identity Property
11-8 Solving Integer Equations
Additional Example 1A: Adding and Subtracting
to Solve Equations
Solve –8 + y = –13. Check your answer.
–8
+8
+
y = –13 y is added to –8.
+ 8 Add 8 to both sides.
y = –5
Check
–8 + y = –13
?
–8 + (–5) = –13
Write the equation.
Substitute –5 for y.
?
–13 = –13  –5 is a solution.
11-8 Solving Integer Equations
Helpful Hint
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.
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 Add 2 to both sides to
undo the subtraction.
n = –6
+2
Check
n – 2 = –8
?
–6 – 2 = –8
?
–8 = –8 
Write the equation.
Substitute –6 for n.
–6 is a solution.
11-8 Solving Integer Equations
Check It Out: Example 1A
Solve –2 + y = –7. Check your answer.
–2
+
y = –7
+2
+2
y is added to –2.
Add 2 to both sides.
y = –5
Check
–2 + y = –7
–2
+
?
(–5) = –7
?
-7 = -7 
Write the equation.
Substitute –5 for y.
–5 is a solution.
11-8 Solving Integer Equations
Check It Out: Example 1B
Solve n – 6 = –14. Check your answer.
n – 6 = –14
+6
+6
6 is subtracted from n.
Add 6 to both sides to undo the
subtraction.
n = –8
Check
n – 6 = –14
?
–8 – 6 = –14
?
–14= –14 
Write the equation.
Substitute –8 for n.
–8 is a solution.
11-8 Solving Integer Equations
Additional Example 2A: Multiplying and Dividing
to Solve Equations
Solve 4m = –20. Check your answer.
-20
4m
___
___
=
4
4
m = –5
Check
4m = –20
?
4(–5) = –20
?
–20 = –20 
m is multiplied by 4. Divide
both sides by 4 to undo the
multiplication.
Write the equation.
Substitute –5 for m.
–5 is a solution.
11-8 Solving Integer Equations
Additional Example 2B: Multiplying and Dividing
to Solve Equations
Solve x = –7. Check your answer.
3
x
__
3•
= 3 • (–7) x is divided by 3. Multiply both
3
sides by 3 to undo the division.
x = –21
Check
x
__
= –7
3
?
–21 ÷ 3 = –7
?
–7 = –7 
Write the equation.
Substitute –21 for x.
–21 is a solution.
11-8 Solving Integer Equations
Check It Out: Example 2A
Solve 3n = –15. Check your answer.
–15
3n
___
= ___
3
3
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.
3(–5) = –15
?
–15 = –15 
–5 is a solution.
11-8 Solving Integer Equations
Check It Out: Example 2B
y = –6. Check your answer.
Solve __
4
y
__
4•
= 4 • (–6) y is divided by 4. Multiply both
4
sides by 4 to undo the division.
y = –24
Check
y
__
= –6
4
?
–24 ÷ 4 = –6
?
–6 = –6 
Write the equation.
Substitute –24 for y.
–24 is a solution.