Solve 5x+6/2+x-8/6=10x-1/4-4x-5/3

$$\frac { 5 x + 6 } { 2 } + \frac { x - 8 } { 6 } = \frac { 10 x - 1 } { 4 } - \frac { 4 x - 5 } { 3 }$$

Solve for x

$$x=-\frac{1}{6}\approx -0.166666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,6,4,3.

$$6\left(5x+6\right)+2\left(x-8\right)=3\left(10x-1\right)-4\left(4x-5\right)$$

Use the distributive property to multiply 6 by 5x+6.

$$30x+36+2\left(x-8\right)=3\left(10x-1\right)-4\left(4x-5\right)$$

Use the distributive property to multiply 2 by x-8.

$$30x+36+2x-16=3\left(10x-1\right)-4\left(4x-5\right)$$

Combine 30x and 2x to get 32x.

$$32x+36-16=3\left(10x-1\right)-4\left(4x-5\right)$$

Subtract 16 from 36 to get 20.

$$32x+20=3\left(10x-1\right)-4\left(4x-5\right)$$

Use the distributive property to multiply 3 by 10x-1.

$$32x+20=30x-3-4\left(4x-5\right)$$

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

$$32x+20=30x-3-16x+20$$

Combine 30x and -16x to get 14x.

$$32x+20=14x-3+20$$

Add -3 and 20 to get 17.

$$32x+20=14x+17$$

Subtract 14x from both sides.

$$32x+20-14x=17$$

Combine 32x and -14x to get 18x.

$$18x+20=17$$

Subtract 20 from both sides.

$$18x=17-20$$

Subtract 20 from 17 to get -3.

$$18x=-3$$

Divide both sides by 18.

$$x=\frac{-3}{18}$$

Reduce the fraction \frac{-3}{18} to lowest terms by extracting and canceling out 3.

$$x=-\frac{1}{6}$$