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

Nov 13, 2015

x = 8

#### Explanation:

x+3=2x−5

You want to isolate the "x" on one side, so subtract "x" from one side and move it over to the other side with "2x."

3 = 2x - x - 5

Then move the -5 to the other side by changing the sign (-5 to +5) and adding it to the other side.

3 + 5 = 2x - x

Solve it and you should result with 8 = x.

Nov 13, 2015

More detail given

#### Explanation:

Given that: $x + 3 = 2 x - 5$

Grouping like terms with $x$ on the right to keep it positive and everything else on the other side.

Add $\textcolor{b l u e}{5}$ to both sides.

$\left(x + 3\right) \textcolor{b l u e}{+ 5} = \left(2 x - 5\right) \textcolor{b l u e}{+ 5}$
The brackets only function is to show what is being changed

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

$x + 8 = 2 x + 0$

Subtract $\textcolor{b l u e}{x}$ from both sides

$\left(x + 8\right) - \textcolor{b l u e}{x} = \left(2 x\right) - \textcolor{b l u e}{x}$

but $2 x \to 2 \text{ of "x " so } 2 x = x + x$

$8 + \left(x \textcolor{b l u e}{- x}\right) = x + \left(x - \textcolor{b l u e}{x}\right)$

$8 + 0 = x + 0$
$8 = x$

Convention is that $x$ is on the left so reverse

$x = 8$
.