# How do you solve 4(x + 0.5) = 2(x - 1.5) ?

Feb 10, 2017

See the entire solution process below:

#### Explanation:

First, expand the terms in parenthesis on each side of the equation:

$\left(4 \times x\right) + \left(4 \times 0.5\right) = \left(2 \times x\right) - \left(2 1.5\right)$

$4 x + 2 = 2 x - 3$

Next, subtract $\textcolor{red}{2}$ and $\textcolor{b l u e}{2 x}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$4 x + 2 - \textcolor{red}{2} - \textcolor{b l u e}{2 x} = 2 x - 3 - \textcolor{red}{2} - \textcolor{b l u e}{2 x}$

$4 x - \textcolor{b l u e}{2 x} + 2 - \textcolor{red}{2} = 2 x - \textcolor{b l u e}{2 x} - 3 - \textcolor{red}{2}$

$2 x + 0 = 0 - 5$

$2 x = - 5$

Now, divide each side of the equation by $\textcolor{red}{2}$ to solve for $x$ while keeping the equation balanced:

$\frac{2 x}{\textcolor{red}{2}} = - \frac{5}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} = - 2.5$

$x - 2.5$