# How do you solve 2.2x - 5= 2( 1.4x + 3)?

Mar 21, 2018

$x = - 18.33 = - \frac{55}{3}$

#### Explanation:

Use order of operations (PEMDAS).
$\textcolor{b l u e}{P}$araentheses
$\textcolor{b l u e}{E}$xponents
$\textcolor{b l u e}{M}$ultiplication/$\textcolor{b l u e}{D}$ivision
$\textcolor{b l u e}{A}$ddition/$\textcolor{b l u e}{S}$ubtraction

1. Solve inside parentheses first. Since $\left(1.4 x + 3\right)$ cannot be simplified any more, skip this step.

2. There are no exponents, so skip this step.

3. Multiply $2 \left(1.4 x + 3\right)$ by distributing the $2$. There is no division, so do not worry about dividing anything.
$2.2 x - 5 = \textcolor{red}{2 \left(1.4 x + 3\right)}$
$2.2 x - 5 = \textcolor{red}{2 \left(1.4 x\right) + 2 \left(3\right)}$
$2.2 x - 5 = \textcolor{red}{2.8 x + 6}$

4. Since we cannot simplify the equation by adding or subtracting, skip this step.

5. Isolate and solve for $x$.
$\textcolor{red}{- 0.6 x} - 5 = 6$
$- 0.6 x = \textcolor{red}{11}$
$x = - \frac{11}{0.6} = - 18.33$

EXTRA STEP: If your teacher wants the answer in fraction form, technically $- \frac{11}{0.6}$ is not correct because we cannot have a decimal in a fraction. Follow the steps below to rewrite it:
$- \frac{11}{\frac{6}{10}} = - \frac{11}{1} \div \frac{6}{10} = - \frac{11}{1} \cdot \frac{10}{6} = - \frac{110}{6} = - \frac{55}{3}$