Solve 3+4/5x-2xleq2/3-x

$$3 + 4 / 5 x - 2 x \leq 2 / 3 - x$$

Solve for x

$$x\geq \frac{35}{3}$$

Solution Steps

Combine \frac{4}{5}x and -2x to get -\frac{6}{5}x.

$$3-\frac{6}{5}x\leq \frac{2}{3}-x$$

Add x to both sides.

$$3-\frac{6}{5}x+x\leq \frac{2}{3}$$

Combine -\frac{6}{5}x and x to get -\frac{1}{5}x.

$$3-\frac{1}{5}x\leq \frac{2}{3}$$

Subtract 3 from both sides.

$$-\frac{1}{5}x\leq \frac{2}{3}-3$$

Convert 3 to fraction \frac{9}{3}.

$$-\frac{1}{5}x\leq \frac{2}{3}-\frac{9}{3}$$

Since \frac{2}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{5}x\leq \frac{2-9}{3}$$

Subtract 9 from 2 to get -7.

$$-\frac{1}{5}x\leq -\frac{7}{3}$$

Multiply both sides by -5, the reciprocal of -\frac{1}{5}. Since -\frac{1}{5} is negative, the inequality direction is changed.

$$x\geq -\frac{7}{3}\left(-5\right)$$

Express -\frac{7}{3}\left(-5\right) as a single fraction.

$$x\geq \frac{-7\left(-5\right)}{3}$$

Multiply -7 and -5 to get 35.

$$x\geq \frac{35}{3}$$