Solve 1-xgeq4-x-1/2

$$1 - x \geq 4 - \frac { x - 1 } { 2 }$$

Solve for x

$$x\leq -7$$

Solution Steps

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

$$2-2x\geq 8-\left(x-1\right)$$

To find the opposite of x-1, find the opposite of each term.

$$2-2x\geq 8-x-\left(-1\right)$$

The opposite of -1 is 1.

$$2-2x\geq 8-x+1$$

Add 8 and 1 to get 9.

$$2-2x\geq 9-x$$

Add x to both sides.

$$2-2x+x\geq 9$$

Combine -2x and x to get -x.

$$2-x\geq 9$$

Subtract 2 from both sides.

$$-x\geq 9-2$$

Subtract 2 from 9 to get 7.

$$-x\geq 7$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\leq -7$$