Solve 3(x/10-1/4)+x=5(x/4-1/10)

$$3 ( \frac { x } { 10 } - \frac { 1 } { 4 } ) + x = 5 ( \frac { x } { 4 } - \frac { 1 } { 10 } )$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 10,4.

$$60\left(\frac{x}{10}-\frac{1}{4}\right)+20x=100\left(\frac{x}{4}-\frac{1}{10}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 4 is 20. Multiply \frac{x}{10} times \frac{2}{2}. Multiply \frac{1}{4} times \frac{5}{5}.

$$60\left(\frac{2x}{20}-\frac{5}{20}\right)+20x=100\left(\frac{x}{4}-\frac{1}{10}\right)$$

Since \frac{2x}{20} and \frac{5}{20} have the same denominator, subtract them by subtracting their numerators.

$$60\times \frac{2x-5}{20}+20x=100\left(\frac{x}{4}-\frac{1}{10}\right)$$

Cancel out 20, the greatest common factor in 60 and 20.

$$3\left(2x-5\right)+20x=100\left(\frac{x}{4}-\frac{1}{10}\right)$$

Use the distributive property to multiply 3 by 2x-5.

$$6x-15+20x=100\left(\frac{x}{4}-\frac{1}{10}\right)$$

Combine 6x and 20x to get 26x.

$$26x-15=100\left(\frac{x}{4}-\frac{1}{10}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 10 is 20. Multiply \frac{x}{4} times \frac{5}{5}. Multiply \frac{1}{10} times \frac{2}{2}.

$$26x-15=100\left(\frac{5x}{20}-\frac{2}{20}\right)$$

Since \frac{5x}{20} and \frac{2}{20} have the same denominator, subtract them by subtracting their numerators.

$$26x-15=100\times \frac{5x-2}{20}$$

Cancel out 20, the greatest common factor in 100 and 20.

$$26x-15=5\left(5x-2\right)$$

Use the distributive property to multiply 5 by 5x-2.

$$26x-15=25x-10$$

Subtract 25x from both sides.

$$26x-15-25x=-10$$

Combine 26x and -25x to get x.

$$x-15=-10$$

Add 15 to both sides.

$$x=-10+15$$

Add -10 and 15 to get 5.

$$x=5$$