Solve 31/2-xleq21/2

$$3 \frac { 1 } { 2 } - x \leq 2 \frac { 1 } { 2 }$$

Solve for x

$$x\geq 1$$

Solution Steps

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

$$3\times 2+1-2x\leq 2\times 2+1$$

Multiply 3 and 2 to get 6.

$$6+1-2x\leq 2\times 2+1$$

Add 6 and 1 to get 7.

$$7-2x\leq 2\times 2+1$$

Multiply 2 and 2 to get 4.

$$7-2x\leq 4+1$$

Add 4 and 1 to get 5.

$$7-2x\leq 5$$

Subtract 7 from both sides.

$$-2x\leq 5-7$$

Subtract 7 from 5 to get -2.

$$-2x\leq -2$$

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

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

Divide -2 by -2 to get 1.

$$x\geq 1$$