Solve 1-3(x-1)leq8-x

$$1 - 3 ( x - 1 ) \leq 8 - x$$

Solve for x

$$x\geq -2$$

Solution Steps

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

$$1-3x+3\leq 8-x$$

Add 1 and 3 to get 4.

$$4-3x\leq 8-x$$

Add x to both sides.

$$4-3x+x\leq 8$$

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

$$4-2x\leq 8$$

Subtract 4 from both sides.

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

Subtract 4 from 8 to get 4.

$$-2x\leq 4$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x\geq \frac{4}{-2}$$

Divide 4 by -2 to get -2.

$$x\geq -2$$