Solve 2(9/8-x/10)+x/3=5

$$2 ( \frac { 9 } { 8 } - \frac { x } { 10 } ) + \frac { x } { 3 } = 5$$

Solve for x

$$x = \frac{165}{8} = 20\frac{5}{8} = 20.625$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 120, the least common multiple of 8,10,3.

$$240\left(\frac{9}{8}-\frac{x}{10}\right)+40x=600$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 10 is 40. Multiply \frac{9}{8} times \frac{5}{5}. Multiply \frac{x}{10} times \frac{4}{4}.

$$240\left(\frac{9\times 5}{40}-\frac{4x}{40}\right)+40x=600$$

Since \frac{9\times 5}{40} and \frac{4x}{40} have the same denominator, subtract them by subtracting their numerators.

$$240\times \frac{9\times 5-4x}{40}+40x=600$$

Do the multiplications in 9\times 5-4x.

$$240\times \frac{45-4x}{40}+40x=600$$

Cancel out 40, the greatest common factor in 240 and 40.

$$6\left(45-4x\right)+40x=600$$

Use the distributive property to multiply 6 by 45-4x.

$$270-24x+40x=600$$

Combine -24x and 40x to get 16x.

$$270+16x=600$$

Subtract 270 from both sides.

$$16x=600-270$$

Subtract 270 from 600 to get 330.

$$16x=330$$

Divide both sides by 16.

$$x=\frac{330}{16}$$

Reduce the fraction \frac{330}{16} to lowest terms by extracting and canceling out 2.

$$x=\frac{165}{8}$$