Solving Multi-Step EquationsWednesday, June 25 2014

StarterSolve the following problems for the variable.

1. −4 + 𝑐 = −5 2. 175 = 20 − 𝑙 3. 1

7𝑥 = 6

4. 3

4𝑦 = 6 5. 2 𝑥 + 4 = 30 6. 2𝑥 + 4 = 30

Goals• I can solve a multi-step equation

• 4 𝑥 − 2 + 3𝑥 = 5𝑥 + 2

• I can find whether an equation has one solution, no solution, or multiple solutions. • How many solutions does 2𝑥 + 10 = −2𝑥 + 30 + 8𝑥 have?

Solving two step equations

1. 4𝑥 − 3 = 17 2. 6𝑥 + 5 = 23 3. 𝑥

4= 6

4. −2 5𝑦 − 9 = −42 5. 𝑏

6+10 = 13 6.

1

6𝑚 − 12 = 5

Solving equations with variables on both sides1. −2𝑎 + 7 = 𝑎 − 8

2. 2𝑛 = 4(𝑛 − 8)

GOAL: You always want to get the variable alone on one side of the equation.

3. What value of x would make the linear equation

4𝑥 + 3 4𝑥 + 7 = 4 7𝑥 + 3 − 3 true? What is the “best” first step and why?

4. What value of 𝑥 would make the following linear equation

true: 20 − 3𝑥 − 9 − 2 = −(−11𝑥 + 1)

5. What value of x would make the following linear equation

true: 1

24𝑥 + 6 − 2 = −(5𝑥 + 9)

6. What value of x would make the following linear equation true: 2 𝑥 + 1 = 2𝑥 − 3

7. What value of x would make the following linear equation

true: 9 4 − 2𝑥 − 3 = 4 − 6(3𝑥 − 5)

8. Write your at least one equation that has no solution.

9. What value of 𝑥 would make the following equation true: 3 𝑥 + 6 = 20 + 3𝑥 − 2

10. What value of 𝑥 would make the following equation true: 3 𝑥 + 1 + 1 + 2𝑥 = 2 2𝑥 + 2 + 𝑥

11. Write your at least one equation that has infinitely many solutions.

Review our GoalsI can solve a multi-step equation

• 4 𝑥 − 2 + 3𝑥 = 5𝑥 + 2

I can find whether an equation has one solution, no solution, or multiple solutions.

• How many solutions does 2𝑥 + 10 = −2𝑥 + 30 + 8𝑥 have?

Summary:

• Solving a multi-step equation:

•One solution looks like….

• Infinitely many solutions look like….

•No solutions look like…

Which of the equations has one solution, no solution, or infinitely many solutions?

A. 7𝑥 − 3 = 5𝑥 + 5B. 7𝑥 − 3 = 7𝑥 + 5C. 7𝑥 − 3 = −3 + 7𝑥

Exit Slip:

1. 3 6𝑥 + 8 = 24 + 18𝑥

2. 12 𝑥 + 8 = 11𝑥 − 5

3. 5𝑥 − 8 = 11 − 7𝑥 + 12𝑥

8 =1

3𝑦 − 6 +

1

3𝑦

2

3𝑎 −

3

4=3

4𝑎

1

2𝑥 + 8 + 10 = −16 +

3

2𝑥

8𝑠 + 3 − 10𝑠 = −2 𝑠 − 2 + 3

𝑎 − 5𝑎 + 1 = 8 − 2(𝑎 − 3)