Solve 1-xleq1/2(4-x)

$$1 - x \leq \frac { 1 } { 2 } ( 4 - x )$$

Solve for x

$$x\geq -2$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 4-x.

$$1-x\leq \frac{1}{2}\times 4+\frac{1}{2}\left(-1\right)x$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$1-x\leq \frac{4}{2}+\frac{1}{2}\left(-1\right)x$$

Divide 4 by 2 to get 2.

$$1-x\leq 2+\frac{1}{2}\left(-1\right)x$$

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

$$1-x\leq 2-\frac{1}{2}x$$

Add \frac{1}{2}x to both sides.

$$1-x+\frac{1}{2}x\leq 2$$

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

$$1-\frac{1}{2}x\leq 2$$

Subtract 1 from both sides.

$$-\frac{1}{2}x\leq 2-1$$

Subtract 1 from 2 to get 1.

$$-\frac{1}{2}x\leq 1$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}. Since -\frac{1}{2} is negative, the inequality direction is changed.

$$x\geq 1\left(-2\right)$$

Multiply 1 and -2 to get -2.

$$x\geq -2$$