# How do you solve 4( x - 2) = x + 7?

Jun 2, 2018

$x = 5$

#### Explanation:

Given: $4 \left(x - 2\right) = x + 7$.

Expand the left side.

$4 x - 8 = x + 7$

Subtract $7$ from both sides.

$4 x - 8 - 7 = x$

$4 x - 15 = x$

Subtract $4 x$ from both sides.

$- 15 = x - 4 x$

$- 15 = - 3 x$

Divide by $- 3$.

$x = \frac{- 15}{-} 3$

$= 5$

Jun 2, 2018

$x = 5$

#### Explanation:

To solve for the variable in the equation $4 \left(x - 2\right) = x + 7$

Begin by eliminating the parenthesis by using the distributive property.

$4 \left(x - 2\right) = x + 7$

$4 x - 8 = x + 7$

$3 x - 8 = 7$

Use the additive inverse to get the $x$ terms on one side of the equation.

$4 x - 8 - x = \cancel{x} + 7 \cancel{- x}$

$3 x - 8 = 7$

Use the additive inverse to get the constant values on the same side of the equation

$3 x \cancel{- 8} \cancel{+ 8} = 7 + 8$

$3 x = 15$

Now use the multiplicative inverse to solve for $x$

$\frac{\cancel{3} x}{\cancel{3}} = \frac{15}{3}$

$x = 5$