Solve 1/4-2/3xgeq7/12

$$\frac { 1 } { 4 } - \frac { 2 } { 3 } x \geq \frac { 7 } { 12 }$$

Solve for x

$$x\leq -\frac{1}{2}$$

Solution Steps

Subtract \frac{1}{4} from both sides.

$$-\frac{2}{3}x\geq \frac{7}{12}-\frac{1}{4}$$

Least common multiple of 12 and 4 is 12. Convert \frac{7}{12} and \frac{1}{4} to fractions with denominator 12.

$$-\frac{2}{3}x\geq \frac{7}{12}-\frac{3}{12}$$

Since \frac{7}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}x\geq \frac{7-3}{12}$$

Subtract 3 from 7 to get 4.

$$-\frac{2}{3}x\geq \frac{4}{12}$$

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

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

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

$$x\leq \frac{1}{3}\left(-\frac{3}{2}\right)$$

Multiply \frac{1}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x\leq \frac{1\left(-3\right)}{3\times 2}$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{3\times 2}.

$$x\leq \frac{-3}{6}$$

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

$$x\leq -\frac{1}{2}$$