Solve -3<1/2-2m

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

Solve for m

$$m<\frac{7}{4}$$

Solution Steps

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

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

Subtract \frac{1}{2} from both sides.

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

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

$$-2m>-\frac{6}{2}-\frac{1}{2}$$

Since -\frac{6}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$-2m>\frac{-6-1}{2}$$

Subtract 1 from -6 to get -7.

$$-2m>-\frac{7}{2}$$

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

$$m<\frac{-\frac{7}{2}}{-2}$$

Express \frac{-\frac{7}{2}}{-2} as a single fraction.

$$m<\frac{-7}{2\left(-2\right)}$$

Multiply 2 and -2 to get -4.

$$m<\frac{-7}{-4}$$

Fraction \frac{-7}{-4} can be simplified to \frac{7}{4} by removing the negative sign from both the numerator and the denominator.

$$m<\frac{7}{4}$$