Solve -3(1-x)+xgeq-(8-2x)+8

$$- 3 ( 1 - x ) + x \geq - ( 8 - 2 x ) + 8$$

Solve for x

$$x\geq \frac{3}{2}$$

Solution Steps

Use the distributive property to multiply -3 by 1-x.

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

Combine 3x and x to get 4x.

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

To find the opposite of 8-2x, find the opposite of each term.

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

The opposite of -2x is 2x.

$$-3+4x\geq -8+2x+8$$

Add -8 and 8 to get 0.

$$-3+4x\geq 2x$$

Subtract 2x from both sides.

$$-3+4x-2x\geq 0$$

Combine 4x and -2x to get 2x.

$$-3+2x\geq 0$$

Add 3 to both sides. Anything plus zero gives itself.

$$2x\geq 3$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x\geq \frac{3}{2}$$