Solve 5x/6-1-3x/5=x-x-7/15-1

$$\frac{ 5x }{ 6 } - \frac{ 1-3x }{ 5 } = x- \frac{ x-7 }{ 15 } -1$$

Solve for x

$$x=-\frac{2}{3}\approx -0.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 6,5,15.

$$5\times 5x-6\left(1-3x\right)=30x-2\left(x-7\right)-30$$

Multiply 5 and 5 to get 25.

$$25x-6\left(1-3x\right)=30x-2\left(x-7\right)-30$$

Use the distributive property to multiply -6 by 1-3x.

$$25x-6+18x=30x-2\left(x-7\right)-30$$

Combine 25x and 18x to get 43x.

$$43x-6=30x-2\left(x-7\right)-30$$

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

$$43x-6=30x-2x+14-30$$

Combine 30x and -2x to get 28x.

$$43x-6=28x+14-30$$

Subtract 30 from 14 to get -16.

$$43x-6=28x-16$$

Subtract 28x from both sides.

$$43x-6-28x=-16$$

Combine 43x and -28x to get 15x.

$$15x-6=-16$$

Add 6 to both sides.

$$15x=-16+6$$

Add -16 and 6 to get -10.

$$15x=-10$$

Divide both sides by 15.

$$x=\frac{-10}{15}$$

Reduce the fraction \frac{-10}{15} to lowest terms by extracting and canceling out 5.

$$x=-\frac{2}{3}$$