# Lesson 6

Strategic Solving

### Problem 1

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

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

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

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

### Solution

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### Problem 2

Solve each equation and check your solution.

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

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

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

### Solution

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### 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.

### Solution

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### Problem 4

The table gives some sample data for two quantities, $$x$$ and $$y$$, that are in a proportional relationship.

1. Complete the table.
2. Write an equation that represents the relationship between $$x$$ and $$y$$ shown in the table.
3. Graph the relationship. Use a scale for the axes that shows all the points in the table.

$$x$$ $$y$$
14 21
64
39
1