Solve x+5/2+1geq-1

$$\frac { x + 5 } { 2 + 1 } \geq - 1$$

Solve for x

$$x\geq -8$$

Solution Steps

Add 2 and 1 to get 3.

$$\frac{x+5}{3}\geq -1$$

Divide each term of x+5 by 3 to get \frac{1}{3}x+\frac{5}{3}.

$$\frac{1}{3}x+\frac{5}{3}\geq -1$$

Subtract \frac{5}{3} from both sides.

$$\frac{1}{3}x\geq -1-\frac{5}{3}$$

Convert -1 to fraction -\frac{3}{3}.

$$\frac{1}{3}x\geq -\frac{3}{3}-\frac{5}{3}$$

Since -\frac{3}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}x\geq \frac{-3-5}{3}$$

Subtract 5 from -3 to get -8.

$$\frac{1}{3}x\geq -\frac{8}{3}$$

Multiply both sides by 3, the reciprocal of \frac{1}{3}. Since \frac{1}{3} is positive, the inequality direction remains the same.

$$x\geq -\frac{8}{3}\times 3$$

Cancel out 3 and 3.

$$x\geq -8$$