1. Algebra /19-20/16
EQ: How do I solve Multi-Step Equations?
HW: pg 89 # 1-35 odd, all (all due on Wednesday)
Bring textbooks tomorrow!!!
HW sheet due this Friday
Warm up: See board

2. Additional Example 1A: Solving Two-Step Equations
Solve the equation. Check your answer.
Since 2x + 1 is divided by 3, multiply both sides by 3 to undo the division.
2x + 1 = 21
Since 1 is added to 2x, subtract 1 from both sides to undo the addition.
–1 –1
2x = 20
Since x is multiplied by 2, divide both sides by 2 to undo the multiplication.
x = 10
The solution set is {10}.

3. Additional Example 1B: Solving Two-Step Equations
Solve the equation. Check your answer.
Since 3x – 4 is divided by 2, multiply both sides by 2 to undo the division.
Since 4 is subtracted from 3x, add 4 to both sides to undo the subtraction.
18 = 3x
Since x is multiplied by 3, divide both sides by 3 to undo the multiplication.
6 = x
The solution set is {6}.

4. Check It Out! Example 1a
Solve the equation. Check your answer.
Since 5m + 13 is divided by 2, multiply both sides by 2 to undo the division.
Since 13 is added to 5m, subtract 13 from both sides to undo the addition.
5m + 13 = 2
–13 –13
5m = –11
Since m is multiplied by 5, divide both sides by 5 to undo the multiplication.
The solution set is

5. You may have to combine like terms or use the Distributive Property before you begin solving.

6. Additional Example 2A: Simplifying Before Solving Equations
Solve 8x – 21 – 5x = –15
8x – 21 – 5x = –15
Use the Commutative Property of Addition. Combine like terms.
8x – 5x – 21 = –15
3x – 21 = –15
Since 21 is subtracted from 3x, add 21 to both sides to undo the subtraction.
+21 = +21
3x = 6
Since x is multiplied by 3, divide both sides by 3 to undo the multiplication.
x = 2
The solution set is {2}.

7. Additional Example 2B: Simplifying Before Solving Equations
Solve 4 = 2x + 5 – 6x
4 = 2x + 5 – 6x
Use the Commutative Property of Addition. Combine like terms.
4 = 2x – 6x + 5
4 = –4x + 5
– –5
–1 = –4x
Since 5 is added to –4x, subtract 5 from both sides to undo the addition.
Since x is multiplied by –4, divide both sides by –4 to undo the multiplication.
The solution set is

8. Check It Out! Example 2a
Solve the equation. Check your answer.
2a + 3 – 8a = 8
Use the Commutative Property of Addition. Combine like terms.
2a – 8a +3 = 8
–6a + 3 = 8
Since 3 is added to –6a, subtract 3 from both sides to undo the addition.
–3 –3
–6a = 5
Since a is multiplied by –6, divide both sides by –6 to undo the multiplication.
The solution set is

9. Check It Out! Example 2c
Solve the equation. Check your answer.
4x – 8 + 2x = 40
4x – 8 + 2x = 40
Use the Commutative Property of Addition. Combine like terms.
4x + 2x – 8 = 40
6x – 8 = 40
Since 8 is subtracted from 6x, add 8 to both sides to undo the subtraction.
6x = 48
Since x is multiplied by 6, divide both sides by 6 to undo the multiplication.
x = 8
The solution set is {8}.

10. You can think of a negative sign as a coefficient of –1.
–(x + 2) = –1(x + 2) and –x = –1x.
Helpful Hint

11. Additional Example 3B: Simplify Using the Distributive Property
Solve the equation.
10y – (4y + 8) = –20
Write subtraction as the addition of the opposite.
10y +(–1)(4y + 8) = –20
10y + (–1)(4y) + (–1)(8) = –20
Distribute –1.
10y – 4y – 8 = –20
Simplify.
6y – 8 = –20
Combine like terms.
Since 8 is subtracted from 6y, add 8 to both sides to undo the subtraction.
6y = –12

12. Additional Example 3B Continued
Solve the equation.
10y – (4y +8) = –20
6y = –12
Since y is multiplied by 6, divide both sides by 6 to undo the multiplication.
y = –2

13. Check It Out! Example 3a
Solve the equation. Check your answer.
3(a + 1) – 4 = 5
3(a + 1) – 4 = 5
Distribute 3.
(3)(a) + (3)(1) – 4 = 5
3a + 3 – 4 = 5
Simplify. Combine like terms.
3a – 1 = 5
Since 1 is subtracted from 3a, add 1 to both sides to undo the subtraction.
3a = 6
Since a is multiplied by 3, divide both sides by 3 to undo the multiplication.
a = 2

14. Check It Out! Example 3b
Solve the equation. Check your answer.
–4(2 – y) = 8
–4(2 – y) = 8
Distribute –4 .
(–4)(2) + (–4)(–y) = 8
Simplify.
–8 + 4y = 8
Since –8 is added to 4y, add 8 to both sides.
4y = 16
Since y is multiplied by 4, divide both sides by 4 to undo the multiplication.
y = 4

15. Check It Out! Example 3c
Solve the equation. Check your answer.
d + 3(d – 4) = 20
d + 3(d – 4) = 20
d + 3(d) + 3(–4) = 20
Distribute 3.
d + 3d – 12 = 20
Simplify.
4d – 12 = 20
Combine like terms.
Since 12 is subtracted from 4d, add 12 to both sides to undo the subtraction.
4d = 32
Since d is multiplied by 4, divide both sides by 4 to undo the multiplication.
d = 8