1. Section 2.3 Solving Multi-Step Equations
Algebra 1

2. Learning Targets Solve multi-step equations
Write and solve multi-step equations in a context
Solve equations with variables on both sides
Solve equations with special solutions (no solutions or many solutions)
Write and solve an equation with variables on both sides

3. Example 1: Solving equations Review
Solve for 𝑥: 11𝑥−4=29
1. 11𝑥=33 (add 4 to both sides)
2. 𝑥=3 (divide both sides by 11)

4. Example 2: Solving equations Review
Solve for 𝑥: 4𝑥+15=51
1. 4𝑥=36 (subtract 15 to both sides)
2. 𝑥=9 (divide both sides by 4)

5. Example 3: Solving equations Review
Find 𝑎: 𝑎+7 8 =5
1. 𝑎+7=40 (multiply both sides by 8)
2. 𝑎=33 (subtract 7 from both sides)

6. Example 4: Solving equations Review
Find 𝑝: 𝑝−25=115
𝑝=140 (add 25 to both sides)
2. 2𝑝=420 (multiply 3 to both sides)
3. 𝑝=210 (divide 2 to both sides)
Alternative: 𝑝=210 multiply 3 2 , the reciprocal, to both sides. Combine steps 2&3 into one step.

7. Example 5: Solving equations Review
Find 5𝑥 9 −11=−51
5𝑥 9 =−40
5𝑥=−360
𝑥=−72

8. Example 6: Writing/Solving equations
If 15 less than 9 times a number is 30, what is the number?
1. 9𝑥−15=30
2. 9𝑥=45 (add 15 to both sides)
3. 𝑥=5 (divide both sides by 9)

9. Example 7: Writing/Solving equations
If 12 more than 2 times a number is -10, what is the number?
1. 2𝑦+12=−10
2. 2𝑦=−22 (subtract 12 from both sides)
3. 𝑦=−11 (divide both sides by 2)

10. Example 8: Writing/Solving equations
Find three consecutive integers with a sum of 21
Integer 1: 𝑛, Integer 2: 𝑛+1, Integer 3: 𝑛+2
𝑛+ 𝑛+1 + 𝑛+2 =21
3𝑛+3=21
3𝑛=18
𝑛=6
Integer 1: 6, Integer 2: 7, Integer 3: 8

11. Example 9: Writing/Solving equations
The product of 9 and the sum of a number and 2 is 27.
1. 9 𝑥+2 =27
2. 9𝑥+18=27 (distribute the 9)
3. 9𝑥=9 (subtract 18 from both sides)
4. 𝑥=1 (divide both sides by 9)
Alternative: 𝑥+2=3 (divide by 9 after step 1), then continue to solve.

12. Exit Ticket for Feedback
1. 10 more than the product of 7 and a number is 31, what is the number? 2. Find three consecutive integers with a sum of −36.