Solve 1/2x+2geq-3/2

$$\frac { 1 } { 2 } x + 2 \geq - \frac { 3 } { 2 }$$

Solve for x

$$x\geq -7$$

Solution Steps

Subtract 2 from both sides.

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

Convert 2 to fraction \frac{4}{2}.

$$\frac{1}{2}x\geq -\frac{3}{2}-\frac{4}{2}$$

Since -\frac{3}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x\geq \frac{-3-4}{2}$$

Subtract 4 from -3 to get -7.

$$\frac{1}{2}x\geq -\frac{7}{2}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}. Since \frac{1}{2} is positive, the inequality direction remains the same.

$$x\geq -\frac{7}{2}\times 2$$

Cancel out 2 and 2.

$$x\geq -7$$