# How do you solve 2(2x+3)-2=5?

Jun 23, 2018

$x = \frac{1}{4}$

#### Explanation:

$2 \left(2 x + 3\right) - 2 = 5$

First, add $\textcolor{b l u e}{2}$ to both sides of the equation:
$2 \left(2 x + 3\right) - 2 \quad \textcolor{b l u e}{+ \quad 2} = 5 \quad \textcolor{b l u e}{+ \quad 2}$

$2 \left(2 x + 3\right) = 7$

Use the distributive property (shown below) to simplify $2 \left(2 x + 3\right)$:

Following this image, we know that:
$\textcolor{b l u e}{2 \left(2 x + 3\right) = \left(2 \cdot 2 x\right) + \left(2 \cdot 3\right) = 4 x + 6}$

Put that back into the equation:
$4 x + 6 = 7$

Subtract $\textcolor{b l u e}{6}$ from both sides:
$4 x + 6 \quad \textcolor{b l u e}{- \quad 6} = 7 \quad \textcolor{b l u e}{- \quad 6}$

$4 x = 1$

Divide both sides by $\textcolor{b l u e}{4}$:
$\frac{4 x}{\textcolor{b l u e}{4}} = \frac{1}{\textcolor{b l u e}{4}}$

Therefore,
$x = \frac{1}{4}$

Hope this helps!