Solve x-5/2leq3/2x

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

Solve for x

$$x\geq -5$$

Solution Steps

Subtract \frac{3}{2}x from both sides.

$$x-\frac{5}{2}-\frac{3}{2}x\leq 0$$

Combine x and -\frac{3}{2}x to get -\frac{1}{2}x.

$$-\frac{1}{2}x-\frac{5}{2}\leq 0$$

Add \frac{5}{2} to both sides. Anything plus zero gives itself.

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

Multiply both sides by -2, the reciprocal of -\frac{1}{2}. Since -\frac{1}{2} is negative, the inequality direction is changed.

$$x\geq \frac{5}{2}\left(-2\right)$$

Express \frac{5}{2}\left(-2\right) as a single fraction.

$$x\geq \frac{5\left(-2\right)}{2}$$

Multiply 5 and -2 to get -10.

$$x\geq \frac{-10}{2}$$

Divide -10 by 2 to get -5.

$$x\geq -5$$