2/3 (2x-1)=5/6 (x+1) What is x?

Nov 8, 2017

$\frac{9}{8}$

Explanation:

$\frac{2}{3} \left(2 x - 1\right) = \frac{5}{6}$
Distribute $\frac{2}{3}$:
$\frac{4}{3} x - \frac{2}{3} = \frac{5}{6}$
Add $\frac{2}{3}$ to both sides:
$\frac{4}{3} x = \frac{5}{6} + \frac{2}{3}$
Divide both sides by 4/3:
$x = \frac{3}{2} \setminus \div \frac{4}{3}$
$x = \frac{9}{8}$

Nov 9, 2017

Distribute then solve for x. x=3

Explanation:

1. $\frac{2}{3} \left(2 x - 1\right) = \frac{5}{6} \left(x + 1\right)$

Multiply each fraction on the outside of the parenthesis by the constants inside the parenthesis.

$\frac{4}{3} x - \frac{2}{3} = \frac{5}{6} x + \frac{5}{6}$

Now add $\frac{2}{3}$ to each side and subtract $\frac{5}{6} x$ from each side.

Find a common denominator and add $\frac{5}{6} \mathmr{and} \frac{2}{3}$
$\frac{5}{6} + \frac{2}{3} = \frac{5}{6} + \frac{4}{6} = \frac{9}{6} = \frac{3}{2}$

Again, find a common denominator and subtract $\frac{4}{3} x \mathmr{and} \frac{5}{6} x$
$\frac{4}{3} x - \frac{5}{6} x = \frac{8}{6} x - \frac{5}{6} x = \frac{3}{6} x = \frac{1}{2} x$

Now solve $\frac{1}{2} x = \frac{3}{2}$

Divide both side by $\frac{1}{2}$
$\frac{\frac{1}{2} x}{\frac{1}{2}} = \frac{\frac{3}{2}}{\frac{1}{2}}$

Multiple the reciprocal $\frac{3}{2} \cdot \frac{2}{1} = 3$

You're left with x=3