Solve x-1/4-2x+5/3=5x-7/6-1

$$\frac { x - 1 } { 4 } - \frac { 2 x + 5 } { 3 } = \frac { 5 x - 7 } { 6 } - 1$$

Solve for x

$$x=\frac{1}{5}=0.2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,3,6.

$$3\left(x-1\right)-4\left(2x+5\right)=2\left(5x-7\right)-12$$

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

$$3x-3-4\left(2x+5\right)=2\left(5x-7\right)-12$$

Use the distributive property to multiply -4 by 2x+5.

$$3x-3-8x-20=2\left(5x-7\right)-12$$

Combine 3x and -8x to get -5x.

$$-5x-3-20=2\left(5x-7\right)-12$$

Subtract 20 from -3 to get -23.

$$-5x-23=2\left(5x-7\right)-12$$

Use the distributive property to multiply 2 by 5x-7.

$$-5x-23=10x-14-12$$

Subtract 12 from -14 to get -26.

$$-5x-23=10x-26$$

Subtract 10x from both sides.

$$-5x-23-10x=-26$$

Combine -5x and -10x to get -15x.

$$-15x-23=-26$$

Add 23 to both sides.

$$-15x=-26+23$$

Add -26 and 23 to get -3.

$$-15x=-3$$

Divide both sides by -15.

$$x=\frac{-3}{-15}$$

Reduce the fraction \frac{-3}{-15} to lowest terms by extracting and canceling out -3.

$$x=\frac{1}{5}$$