# Solving 2-Step Equations

## Review how to solve 2-step equations using rules of equality.

Solve the following 2 equations.

1. $$8(4x - 7.5) = 84$$

2. $$-7 = \frac{{y - 9}}{8}$$

1. $$8(4x - 7.5) = 84$$

First, we'll distribute $$8$$ to $$4x - 7.5$$:

$8 \cdot 4x - 8 \cdot 7.5 = 84$

This simplifies to:

$32x - 60 = 84$

Next, let's isolate the variable $$x$$ by adding $$60$$ to both sides:

$32x - 60 + 60 = 84 + 60$

Which simplifies to:

$32x = 144$

Now, divide both sides by $$32$$ to solve for $$x$$:

$\frac{32x}{32} = \frac{144}{32}$

This simplifies to:

$x = \frac{144}{32} = 4.5$

So, the solution to the equation $$8(4x - 7.5) = 84$$ is $$x = 4.5$$.

2. $$-7 = \frac{y - 9}{8}$$

To solve for $$y$$, we'll first isolate the fraction term by multiplying both sides by $$8$$:

$8 \cdot (-7) = 8 \cdot \frac{y - 9}{8}$

This simplifies to:

$-56 = y - 9$

Next, we'll isolate $$y$$ by adding $$9$$ to both sides:

$-56 + 9 = y - 9 + 9$

Which simplifies to:

$-47 = y$

So, the solution to the equation $$-7 = \frac{y - 9}{8}$$ is $$y = -47$$.

Let me know if you need further clarification on any step!