Solve -3/2x-5leq1/2x+7/8

$$- \frac { 3 } { 2 } x - 5 \leq \frac { 1 } { 2 } x + \frac { 7 } { 8 }$$

Solve for x

$$x\geq -\frac{47}{16}$$

Solution Steps

Subtract \frac{1}{2}x from both sides.

$$-\frac{3}{2}x-5-\frac{1}{2}x\leq \frac{7}{8}$$

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

$$-2x-5\leq \frac{7}{8}$$

Add 5 to both sides.

$$-2x\leq \frac{7}{8}+5$$

Convert 5 to fraction \frac{40}{8}.

$$-2x\leq \frac{7}{8}+\frac{40}{8}$$

Since \frac{7}{8} and \frac{40}{8} have the same denominator, add them by adding their numerators.

$$-2x\leq \frac{7+40}{8}$$

Add 7 and 40 to get 47.

$$-2x\leq \frac{47}{8}$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x\geq \frac{\frac{47}{8}}{-2}$$

Express \frac{\frac{47}{8}}{-2} as a single fraction.

$$x\geq \frac{47}{8\left(-2\right)}$$

Multiply 8 and -2 to get -16.

$$x\geq \frac{47}{-16}$$

Fraction \frac{47}{-16} can be rewritten as -\frac{47}{16} by extracting the negative sign.

$$x\geq -\frac{47}{16}$$