# How do you solve  6-5(2x - 3) = 4x+7?

May 3, 2018

$x = 1$

#### Explanation:

$1$ Expand:
$6 - 10 x + 15 = 4 x + 7$

$2$ Simplify $6 - 10 x + 15$ to $- 10 x + 21$:
$- 10 x + 21 = 4 x + 7$

$3$ Add $10 x$ to both sides:
$21 = 4 x + 7 + 10 x$

$4$ Simplify $4 x + 7 + 10 x$ to $14 x + 7$:
$21 = 14 x + 7$

$5$ Subtract $7$ from both sides:
$21 - 7 = 14 x$

$6$ Simplify $21 - 7$ to $14$
$14 = 14 x$

$7$ Divide both sides by $14$:
$1 = x$

$8$ Switch sides:
$x = 1$

May 3, 2018

$x = 1$

#### Explanation:

$6 - 5 \left(2 x - 3\right) = 4 x + 7$

Distribute:
$6 - 10 x + 15 = 4 x + 7$

Simplify the left side:
$21 - 10 x = 4 x + 7$

Subtract $\textcolor{b l u e}{7}$ from both sides of the equation:
$21 - 10 x \quad \textcolor{b l u e}{- \quad 7} = 4 x + 7 \quad \textcolor{b l u e}{- \quad 7}$

$14 - 10 x = 4 x$

Add $\textcolor{b l u e}{10 x}$ to both sides of the equation:
$14 - 10 x \quad \textcolor{b l u e}{+ \quad 10 x} = 4 x \quad \textcolor{b l u e}{+ \quad 10 x}$

$14 = 14 x$

Divide both sides by $\textcolor{b l u e}{14}$:
$\frac{14}{\textcolor{b l u e}{14}} = \frac{14 x}{\textcolor{b l u e}{14}}$

$1 = x$

So
$x = 1$

Hope this helps!