Solve 20*(x/5-3/4)-3x/5=10*(1/5+frac{x}{4})+1

$$20 \times ( \frac{ x }{ 5 } - \frac{ 3 }{ 4 } )- \frac{ 3x }{ 5 } =10 \times ( \frac{ 1 }{ 5 } + \frac{ x }{ 4 } )+1$$

Solve for x

$$x=20$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 5,4.

$$400\left(\frac{x}{5}-\frac{3}{4}\right)-4\times 3x=200\left(\frac{1}{5}+\frac{x}{4}\right)+20$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 4 is 20. Multiply \frac{x}{5} times \frac{4}{4}. Multiply \frac{3}{4} times \frac{5}{5}.

$$400\left(\frac{4x}{20}-\frac{3\times 5}{20}\right)-4\times 3x=200\left(\frac{1}{5}+\frac{x}{4}\right)+20$$

Since \frac{4x}{20} and \frac{3\times 5}{20} have the same denominator, subtract them by subtracting their numerators.

$$400\times \frac{4x-3\times 5}{20}-4\times 3x=200\left(\frac{1}{5}+\frac{x}{4}\right)+20$$

Do the multiplications in 4x-3\times 5.

$$400\times \frac{4x-15}{20}-4\times 3x=200\left(\frac{1}{5}+\frac{x}{4}\right)+20$$

Cancel out 20, the greatest common factor in 400 and 20.

$$20\left(4x-15\right)-4\times 3x=200\left(\frac{1}{5}+\frac{x}{4}\right)+20$$

Use the distributive property to multiply 20 by 4x-15.

$$80x-300-4\times 3x=200\left(\frac{1}{5}+\frac{x}{4}\right)+20$$

Multiply -4 and 3 to get -12.

$$80x-300-12x=200\left(\frac{1}{5}+\frac{x}{4}\right)+20$$

Combine 80x and -12x to get 68x.

$$68x-300=200\left(\frac{1}{5}+\frac{x}{4}\right)+20$$

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

$$68x-300=200\left(\frac{4}{20}+\frac{5x}{20}\right)+20$$

Since \frac{4}{20} and \frac{5x}{20} have the same denominator, add them by adding their numerators.

$$68x-300=200\times \frac{4+5x}{20}+20$$

Cancel out 20, the greatest common factor in 200 and 20.

$$68x-300=10\left(4+5x\right)+20$$

Use the distributive property to multiply 10 by 4+5x.

$$68x-300=40+50x+20$$

Add 40 and 20 to get 60.

$$68x-300=60+50x$$

Subtract 50x from both sides.

$$68x-300-50x=60$$

Combine 68x and -50x to get 18x.

$$18x-300=60$$

Add 300 to both sides.

$$18x=60+300$$

Add 60 and 300 to get 360.

$$18x=360$$

Divide both sides by 18.

$$x=\frac{360}{18}$$

Divide 360 by 18 to get 20.

$$x=20$$