Solve 2(10x+20)-5(8x-12)-22=4(3x-12)+3(12x-8)+14

$$2 ( 10 x + 20 ) - 5 ( 8 x - 12 ) - 22 = 4 ( 3 x - 12 ) + 3 ( 12 x - 8 ) + 14$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 10x+20.

$$20x+40-5\left(8x-12\right)-22=4\left(3x-12\right)+3\left(12x-8\right)+14$$

Use the distributive property to multiply -5 by 8x-12.

$$20x+40-40x+60-22=4\left(3x-12\right)+3\left(12x-8\right)+14$$

Combine 20x and -40x to get -20x.

$$-20x+40+60-22=4\left(3x-12\right)+3\left(12x-8\right)+14$$

Add 40 and 60 to get 100.

$$-20x+100-22=4\left(3x-12\right)+3\left(12x-8\right)+14$$

Subtract 22 from 100 to get 78.

$$-20x+78=4\left(3x-12\right)+3\left(12x-8\right)+14$$

Use the distributive property to multiply 4 by 3x-12.

$$-20x+78=12x-48+3\left(12x-8\right)+14$$

Use the distributive property to multiply 3 by 12x-8.

$$-20x+78=12x-48+36x-24+14$$

Combine 12x and 36x to get 48x.

$$-20x+78=48x-48-24+14$$

Subtract 24 from -48 to get -72.

$$-20x+78=48x-72+14$$

Add -72 and 14 to get -58.

$$-20x+78=48x-58$$

Subtract 48x from both sides.

$$-20x+78-48x=-58$$

Combine -20x and -48x to get -68x.

$$-68x+78=-58$$

Subtract 78 from both sides.

$$-68x=-58-78$$

Subtract 78 from -58 to get -136.

$$-68x=-136$$

Divide both sides by -68.

$$x=\frac{-136}{-68}$$

Divide -136 by -68 to get 2.

$$x=2$$