Solve -3(2x-5)+7x-14+x-4+2(10+2x)=18-11x+4(2-x+4x)-0.5x+1/2x-19

$$- 3 ( 2 x - 5 ) + 7 x - 14 + x - 4 + 2 ( 10 + 2 x ) = 18 - 11 x + 4 ( 2 - x + 4 x ) - 0.5 x + \frac { 1 } { 2 } x - 19$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by 2x-5.

$$-6x+15+7x-14+x-4+2\left(10+2x\right)=18-11x+4\left(2-x+4x\right)-0.5x+\frac{1}{2}x-19$$

Combine -6x and 7x to get x.

$$x+15-14+x-4+2\left(10+2x\right)=18-11x+4\left(2-x+4x\right)-0.5x+\frac{1}{2}x-19$$

Subtract 14 from 15 to get 1.

$$x+1+x-4+2\left(10+2x\right)=18-11x+4\left(2-x+4x\right)-0.5x+\frac{1}{2}x-19$$

Combine x and x to get 2x.

$$2x+1-4+2\left(10+2x\right)=18-11x+4\left(2-x+4x\right)-0.5x+\frac{1}{2}x-19$$

Subtract 4 from 1 to get -3.

$$2x-3+2\left(10+2x\right)=18-11x+4\left(2-x+4x\right)-0.5x+\frac{1}{2}x-19$$

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

$$2x-3+20+4x=18-11x+4\left(2-x+4x\right)-0.5x+\frac{1}{2}x-19$$

Add -3 and 20 to get 17.

$$2x+17+4x=18-11x+4\left(2-x+4x\right)-0.5x+\frac{1}{2}x-19$$

Combine 2x and 4x to get 6x.

$$6x+17=18-11x+4\left(2-x+4x\right)-0.5x+\frac{1}{2}x-19$$

Combine -x and 4x to get 3x.

$$6x+17=18-11x+4\left(2+3x\right)-0.5x+\frac{1}{2}x-19$$

Use the distributive property to multiply 4 by 2+3x.

$$6x+17=18-11x+8+12x-0.5x+\frac{1}{2}x-19$$

Add 18 and 8 to get 26.

$$6x+17=26-11x+12x-0.5x+\frac{1}{2}x-19$$

Combine -11x and 12x to get x.

$$6x+17=26+x-0.5x+\frac{1}{2}x-19$$

Combine x and -0.5x to get 0.5x.

$$6x+17=26+0.5x+\frac{1}{2}x-19$$

Combine 0.5x and \frac{1}{2}x to get x.

$$6x+17=26+x-19$$

Subtract 19 from 26 to get 7.

$$6x+17=7+x$$

Subtract x from both sides.

$$6x+17-x=7$$

Combine 6x and -x to get 5x.

$$5x+17=7$$

Subtract 17 from both sides.

$$5x=7-17$$

Subtract 17 from 7 to get -10.

$$5x=-10$$

Divide both sides by 5.

$$x=\frac{-10}{5}$$

Divide -10 by 5 to get -2.

$$x=-2$$