Solve (3/4-3/4x2/4)geq1/5*5

$$( \frac { 3 } { 4 } - \frac { 3 } { 4 } x \frac { 2 } { 4 } ) \geq \frac { 1 } { 5 } \times 5$$

Solve for x

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

Solution Steps

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}-\frac{3}{4}x\times \frac{1}{2}\geq \frac{1}{5}\times 5$$

Multiply \frac{3}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4}-\frac{3\times 1}{4\times 2}x\geq \frac{1}{5}\times 5$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 2}.

$$\frac{3}{4}-\frac{3}{8}x\geq \frac{1}{5}\times 5$$

Cancel out 5 and 5.

$$\frac{3}{4}-\frac{3}{8}x\geq 1$$

Subtract \frac{3}{4} from both sides.

$$-\frac{3}{8}x\geq 1-\frac{3}{4}$$

Convert 1 to fraction \frac{4}{4}.

$$-\frac{3}{8}x\geq \frac{4}{4}-\frac{3}{4}$$

Since \frac{4}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{8}x\geq \frac{4-3}{4}$$

Subtract 3 from 4 to get 1.

$$-\frac{3}{8}x\geq \frac{1}{4}$$

Multiply both sides by -\frac{8}{3}, the reciprocal of -\frac{3}{8}. Since -\frac{3}{8} is negative, the inequality direction is changed.

$$x\leq \frac{1}{4}\left(-\frac{8}{3}\right)$$

Multiply \frac{1}{4} times -\frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$x\leq \frac{1\left(-8\right)}{4\times 3}$$

Do the multiplications in the fraction \frac{1\left(-8\right)}{4\times 3}.

$$x\leq \frac{-8}{12}$$

Reduce the fraction \frac{-8}{12} to lowest terms by extracting and canceling out 4.

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