Solve x-4(x+2)leq2x-[x-(3-4x)]

$$x - 4 ( x + 2 ) \leq 2 x - [ x - ( 3 - 4 x ) ]$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

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

$$x-4x-8\leq 2x-\left(x-\left(3-4x\right)\right)$$

Combine x and -4x to get -3x.

$$-3x-8\leq 2x-\left(x-\left(3-4x\right)\right)$$

To find the opposite of 3-4x, find the opposite of each term.

$$-3x-8\leq 2x-\left(x-3-\left(-4x\right)\right)$$

The opposite of -4x is 4x.

$$-3x-8\leq 2x-\left(x-3+4x\right)$$

Combine x and 4x to get 5x.

$$-3x-8\leq 2x-\left(5x-3\right)$$

To find the opposite of 5x-3, find the opposite of each term.

$$-3x-8\leq 2x-5x-\left(-3\right)$$

The opposite of -3 is 3.

$$-3x-8\leq 2x-5x+3$$

Combine 2x and -5x to get -3x.

$$-3x-8\leq -3x+3$$

Add 3x to both sides.

$$-3x-8+3x\leq 3$$

Combine -3x and 3x to get 0.

$$-8\leq 3$$

This is true for any x.

$$x\in \mathrm{R}$$