Solve (2/3(7/8-x/4)-3/8=frac{5}{8})

$$( \frac { 2 } { 3 } ( \frac { 7 } { 8 } - \frac { x } { 4 } ) - \frac { 3 } { 8 } = \frac { 5 } { 8 } )$$

Solve for x

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 3,8,4.

$$16\left(\frac{7}{8}-\frac{x}{4}\right)-9=15$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 4 is 8. Multiply \frac{x}{4} times \frac{2}{2}.

$$16\left(\frac{7}{8}-\frac{2x}{8}\right)-9=15$$

Since \frac{7}{8} and \frac{2x}{8} have the same denominator, subtract them by subtracting their numerators.

$$16\times \frac{7-2x}{8}-9=15$$

Cancel out 8, the greatest common factor in 16 and 8.

$$2\left(7-2x\right)-9=15$$

Use the distributive property to multiply 2 by 7-2x.

$$14-4x-9=15$$

Subtract 9 from 14 to get 5.

$$5-4x=15$$

Subtract 5 from both sides.

$$-4x=15-5$$

Subtract 5 from 15 to get 10.

$$-4x=10$$

Divide both sides by -4.

$$x=\frac{10}{-4}$$

Reduce the fraction \frac{10}{-4} to lowest terms by extracting and canceling out 2.

$$x=-\frac{5}{2}$$