Solve -2a-1geq-1/2a-3

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

Solve for a

$$a\leq \frac{4}{3}$$

Solution Steps

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

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

Combine -2a and \frac{1}{2}a to get -\frac{3}{2}a.

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

Add 1 to both sides.

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

Add -3 and 1 to get -2.

$$-\frac{3}{2}a\geq -2$$

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}. Since -\frac{3}{2} is negative, the inequality direction is changed.

$$a\leq -2\left(-\frac{2}{3}\right)$$

Express -2\left(-\frac{2}{3}\right) as a single fraction.

$$a\leq \frac{-2\left(-2\right)}{3}$$

Multiply -2 and -2 to get 4.

$$a\leq \frac{4}{3}$$