# How do you solve 3x+4=5x+2 ?

Nov 7, 2015

Subtract $3 x + 2$ from both sides, then divide by $2$ to find $x = 1$

#### Explanation:

Isolate $x$ on one side of the equation, by subtracting $3 x + 2$ from both sides to get:

$2 = 2 x$

(Since $3 x + 4 - \left(3 x + 2\right) = 3 x - 3 x + 4 - 2 = 2$ and $5 x + 2 - \left(3 x + 2\right) = 5 x - 3 x + 2 - 2 = 2 x$)

Then divide both sides by $2$ to get $1 = x$. That is $x = 1$.

Alternatively, just notice that $3 + 4 = 7 = 5 + 2$, so $x = 1$ will work.

Nov 7, 2015
• Get variables on one side, and constants on the other side
$x = 1$

#### Explanation:

$3 x + 4 = 5 x + 2$

Subtract 5x from both sides so you remove the variable on the right:
$3 x - 5 x + 4 = 5 x - 5 x + 2$

$- 2 x + 4 = 2$
$- 2 x + 4 - 4 = 2 - 4$
$- 2 x = - 2$
To only get one $x$, divide both sides by $- 2$:
$\frac{- 2 x}{-} 2 = \frac{- 2}{-} 2 \to \frac{\cancel{- 2} x}{\cancel{- 2}} = \frac{\cancel{- 2}}{\cancel{- 2}} \to x = 1$