# Lesson 14

Strategic Solving

### Problem 1

Solve each of these equations. Explain or show your reasoning.

$$2b+8-5b+3=\text-13+8b-5$$

$$2x+7-5x+8=3(5+6x)-12x$$

$$2c-3=2(6-c)+7c$$

### Problem 2

Solve each equation and check your solution.

$$\text-3w-4=w+3$$

$$3(3-3x)=2(x+3)-30$$

$$\frac13(z+4)-6=\frac23(5-z)$$

### Problem 3

Elena said the equation $$9x+15=3x+15$$ has no solutions because $$9x$$ is greater than $$3x$$. Do you agree with Elena? Explain your reasoning.

### Problem 4

Which of the changes would keep the hanger in balance?

Select all that apply.

A:

Adding two circles on the left and a square on the right

B:

Adding 2 triangles to each side

C:

Adding two circles on the right and a square on the left

D:

Adding a circle on the left and a square on the right

E:

Adding a triangle on the left and a square on the right