Solve 5left(2x/3-3x/5right)+1=2x-2(x-1)

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

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$75\left(\frac{2x}{3}-\frac{3x}{5}\right)+15=30x-30\left(x-1\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{2x}{3} times \frac{5}{5}. Multiply \frac{3x}{5} times \frac{3}{3}.

$$75\left(\frac{5\times 2x}{15}-\frac{3\times 3x}{15}\right)+15=30x-30\left(x-1\right)$$

Since \frac{5\times 2x}{15} and \frac{3\times 3x}{15} have the same denominator, subtract them by subtracting their numerators.

$$75\times \frac{5\times 2x-3\times 3x}{15}+15=30x-30\left(x-1\right)$$

Do the multiplications in 5\times 2x-3\times 3x.

$$75\times \frac{10x-9x}{15}+15=30x-30\left(x-1\right)$$

Combine like terms in 10x-9x.

$$75\times \frac{x}{15}+15=30x-30\left(x-1\right)$$

Cancel out 15, the greatest common factor in 75 and 15.

$$5x+15=30x-30\left(x-1\right)$$

Use the distributive property to multiply -30 by x-1.

$$5x+15=30x-30x+30$$

Combine 30x and -30x to get 0.

$$5x+15=30$$

Subtract 15 from both sides.

$$5x=30-15$$

Subtract 15 from 30 to get 15.

$$5x=15$$

Divide both sides by 5.

$$x=\frac{15}{5}$$

Divide 15 by 5 to get 3.

$$x=3$$