Solve -3-2m/3leq-1/2

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

Solve for m

$$m\geq -\frac{3}{4}$$

Solution Steps

Multiply both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$-3-2m\leq -\frac{1}{2}\times 3$$

Express -\frac{1}{2}\times 3 as a single fraction.

$$-3-2m\leq \frac{-3}{2}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$-3-2m\leq -\frac{3}{2}$$

Add 3 to both sides.

$$-2m\leq -\frac{3}{2}+3$$

Convert 3 to fraction \frac{6}{2}.

$$-2m\leq -\frac{3}{2}+\frac{6}{2}$$

Since -\frac{3}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$-2m\leq \frac{-3+6}{2}$$

Add -3 and 6 to get 3.

$$-2m\leq \frac{3}{2}$$

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

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

Express \frac{\frac{3}{2}}{-2} as a single fraction.

$$m\geq \frac{3}{2\left(-2\right)}$$

Multiply 2 and -2 to get -4.

$$m\geq \frac{3}{-4}$$

Fraction \frac{3}{-4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$m\geq -\frac{3}{4}$$