11-8 Solving Integer Equations Warm Up Use 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 = 20 x 5 __
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 __