# How do you solve 4x-10=7-2x?

Mar 11, 2018

$x = \frac{17}{6}$

#### Explanation:

Given: $4 x - 10 = 7 - 2 x$

Adding $2 x$ to both sides, we get

$4 x - 10 + 2 x = 7 - \textcolor{red}{\cancel{\textcolor{b l a c k}{2 x}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{2 x}}}$

$\implies 6 x - 10 = 7$

Adding $10$ to both sides, we have

$\implies 6 x - \textcolor{red}{\cancel{\textcolor{b l a c k}{10}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{10}}} = 7 + 10$

$\implies 6 x = 17$

Final step is to divide by $6$ on both sides.

$\implies \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}}} = \frac{17}{6}$

$\implies x = \frac{17}{6}$

Mar 11, 2018

$x$ = $\frac{17}{6}$

#### Explanation:

Add 2$x$ and 10 to both sides to get 6$x$ = 17

Then divide both sides by 6 to leave $x$ alone on one side, giving $x$ = $\frac{17}{6}$

Mar 11, 2018

$x = \frac{17}{6}$

#### Explanation:

Move all the $x$ terms to one side and the numbers to the other side.

$4 x - 10 = 7 - 2 x \text{ } \leftarrow$ add $2 x$ to each side

$4 x - 10 \textcolor{b l u e}{+ 2 x} = 7 - 2 x \textcolor{b l u e}{+ 2 x}$

$6 x - 10 \textcolor{red}{+ 10} = 7 - 10 \textcolor{red}{+ 10} \text{ }$add$\textcolor{red}{10}$ to both sides

$6 x = 17$

$\frac{6 x}{6} = \frac{17}{6} \text{ } \leftarrow \div 6$ on both sides

$x = \frac{17}{6}$