Solve 4x+20/24-12x+24/24=x+1/2+x+8/4

$$\frac{ 4x+20 }{ 24 } - \frac{ 12x+24 }{ 24 } = \frac{ x+1 }{ 2 } + \frac{ x+8 }{ 4 }$$

Solve for x

$$x = -\frac{32}{13} = -2\frac{6}{13} \approx -2.461538462$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 24,2,4.

$$4x+20-\left(12x+24\right)=12\left(x+1\right)+6\left(x+8\right)$$

To find the opposite of 12x+24, find the opposite of each term.

$$4x+20-12x-24=12\left(x+1\right)+6\left(x+8\right)$$

Combine 4x and -12x to get -8x.

$$-8x+20-24=12\left(x+1\right)+6\left(x+8\right)$$

Subtract 24 from 20 to get -4.

$$-8x-4=12\left(x+1\right)+6\left(x+8\right)$$

Use the distributive property to multiply 12 by x+1.

$$-8x-4=12x+12+6\left(x+8\right)$$

Use the distributive property to multiply 6 by x+8.

$$-8x-4=12x+12+6x+48$$

Combine 12x and 6x to get 18x.

$$-8x-4=18x+12+48$$

Add 12 and 48 to get 60.

$$-8x-4=18x+60$$

Subtract 18x from both sides.

$$-8x-4-18x=60$$

Combine -8x and -18x to get -26x.

$$-26x-4=60$$

Add 4 to both sides.

$$-26x=60+4$$

Add 60 and 4 to get 64.

$$-26x=64$$

Divide both sides by -26.

$$x=\frac{64}{-26}$$

Reduce the fraction \frac{64}{-26} to lowest terms by extracting and canceling out 2.

$$x=-\frac{32}{13}$$