Solve 4/7xgeq1/4(5x-64)

$$\frac { 4 } { 7 } x \geq \frac { 1 } { 4 } ( 5 x - 64 )$$

Solve for x

$$x\leq \frac{448}{19}$$

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 5x-64.

$$\frac{4}{7}x\geq \frac{1}{4}\times 5x+\frac{1}{4}\left(-64\right)$$

Multiply \frac{1}{4} and 5 to get \frac{5}{4}.

$$\frac{4}{7}x\geq \frac{5}{4}x+\frac{1}{4}\left(-64\right)$$

Multiply \frac{1}{4} and -64 to get \frac{-64}{4}.

$$\frac{4}{7}x\geq \frac{5}{4}x+\frac{-64}{4}$$

Divide -64 by 4 to get -16.

$$\frac{4}{7}x\geq \frac{5}{4}x-16$$

Subtract \frac{5}{4}x from both sides.

$$\frac{4}{7}x-\frac{5}{4}x\geq -16$$

Combine \frac{4}{7}x and -\frac{5}{4}x to get -\frac{19}{28}x.

$$-\frac{19}{28}x\geq -16$$

Multiply both sides by -\frac{28}{19}, the reciprocal of -\frac{19}{28}. Since -\frac{19}{28} is negative, the inequality direction is changed.

$$x\leq -16\left(-\frac{28}{19}\right)$$

Express -16\left(-\frac{28}{19}\right) as a single fraction.

$$x\leq \frac{-16\left(-28\right)}{19}$$

Multiply -16 and -28 to get 448.

$$x\leq \frac{448}{19}$$