Solve -5x-1/6geq3/2?

$$- 5 x - \frac { 1 } { 6 } \geq \frac { 3 } { 2 } ?$$

Solve for x

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

Solution Steps

Add \frac{1}{6} to both sides.

$$-5x\geq \frac{3}{2}+\frac{1}{6}$$

Least common multiple of 2 and 6 is 6. Convert \frac{3}{2} and \frac{1}{6} to fractions with denominator 6.

$$-5x\geq \frac{9}{6}+\frac{1}{6}$$

Since \frac{9}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$-5x\geq \frac{9+1}{6}$$

Add 9 and 1 to get 10.

$$-5x\geq \frac{10}{6}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$-5x\geq \frac{5}{3}$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

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

Express \frac{\frac{5}{3}}{-5} as a single fraction.

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

Multiply 3 and -5 to get -15.

$$x\leq \frac{5}{-15}$$

Reduce the fraction \frac{5}{-15} to lowest terms by extracting and canceling out 5.

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