Solve -8(1-x)+xleq-(4-2x)+4

$$- 8 ( 1 - x ) + x \leq - ( 4 - 2 x ) + 4$$

Solve for x

$$x\leq \frac{8}{7}$$

Solution Steps

Use the distributive property to multiply -8 by 1-x.

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

Combine 8x and x to get 9x.

$$-8+9x\leq -\left(4-2x\right)+4$$

To find the opposite of 4-2x, find the opposite of each term.

$$-8+9x\leq -4-\left(-2x\right)+4$$

The opposite of -2x is 2x.

$$-8+9x\leq -4+2x+4$$

Add -4 and 4 to get 0.

$$-8+9x\leq 2x$$

Subtract 2x from both sides.

$$-8+9x-2x\leq 0$$

Combine 9x and -2x to get 7x.

$$-8+7x\leq 0$$

Add 8 to both sides. Anything plus zero gives itself.

$$7x\leq 8$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$x\leq \frac{8}{7}$$