Solve x-5leq3/2(3x-2)

$$x - 5 \leq \frac { 3 } { 2 } ( 3 x - 2 )$$

Solve for x

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

Solution Steps

Use the distributive property to multiply \frac{3}{2} by 3x-2.

$$x-5\leq \frac{3}{2}\times 3x+\frac{3}{2}\left(-2\right)$$

Express \frac{3}{2}\times 3 as a single fraction.

$$x-5\leq \frac{3\times 3}{2}x+\frac{3}{2}\left(-2\right)$$

Multiply 3 and 3 to get 9.

$$x-5\leq \frac{9}{2}x+\frac{3}{2}\left(-2\right)$$

Express \frac{3}{2}\left(-2\right) as a single fraction.

$$x-5\leq \frac{9}{2}x+\frac{3\left(-2\right)}{2}$$

Multiply 3 and -2 to get -6.

$$x-5\leq \frac{9}{2}x+\frac{-6}{2}$$

Divide -6 by 2 to get -3.

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

Subtract \frac{9}{2}x from both sides.

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

Combine x and -\frac{9}{2}x to get -\frac{7}{2}x.

$$-\frac{7}{2}x-5\leq -3$$

Add 5 to both sides.

$$-\frac{7}{2}x\leq -3+5$$

Add -3 and 5 to get 2.

$$-\frac{7}{2}x\leq 2$$

Multiply both sides by -\frac{2}{7}, the reciprocal of -\frac{7}{2}. Since -\frac{7}{2} is negative, the inequality direction is changed.

$$x\geq 2\left(-\frac{2}{7}\right)$$

Express 2\left(-\frac{2}{7}\right) as a single fraction.

$$x\geq \frac{2\left(-2\right)}{7}$$

Multiply 2 and -2 to get -4.

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

Fraction \frac{-4}{7} can be rewritten as -\frac{4}{7} by extracting the negative sign.

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