# How do you solve 2x+3=3x-4?

Jul 19, 2016

With practice you can do these quicker as you learn the shortcut.

$x = 7$

#### Explanation:

Objective is to have a single $x$ on one side of the = and everything else on the other side.

Given:$\text{ } \textcolor{g r e e n}{2 x + 3 = 3 x - 4}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Step 1 ")color(brown)("Having all the "x" terms on one side of =}}$

Subtract $\textcolor{red}{2 x}$ from both sides

$\textcolor{g r e e n}{2 x \textcolor{red}{- 2 x} + 3 = 3 x \textcolor{red}{- 2 x} - 4}$

$0 + 3 = x - 4$

Swap round

$x - 4 = 3$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Step 2 ")color(brown)("Have just "x" on the left of =}}$

Add $\textcolor{red}{4}$ to both sides

$\textcolor{g r e e n}{x - 4 \textcolor{red}{+ 4} = 3 \textcolor{red}{+ 4}}$

$x = 7$