Solve -1/5x-2geq1/2x+3/4

$$- \frac { 1 } { 5 } x - 2 \geq \frac { 1 } { 2 } x + \frac { 3 } { 4 }$$

Solve for x

$$x\leq -\frac{55}{14}$$

Solution Steps

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

$$-\frac{1}{5}x-2-\frac{1}{2}x\geq \frac{3}{4}$$

Combine -\frac{1}{5}x and -\frac{1}{2}x to get -\frac{7}{10}x.

$$-\frac{7}{10}x-2\geq \frac{3}{4}$$

Add 2 to both sides.

$$-\frac{7}{10}x\geq \frac{3}{4}+2$$

Convert 2 to fraction \frac{8}{4}.

$$-\frac{7}{10}x\geq \frac{3}{4}+\frac{8}{4}$$

Since \frac{3}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$-\frac{7}{10}x\geq \frac{3+8}{4}$$

Add 3 and 8 to get 11.

$$-\frac{7}{10}x\geq \frac{11}{4}$$

Multiply both sides by -\frac{10}{7}, the reciprocal of -\frac{7}{10}. Since -\frac{7}{10} is negative, the inequality direction is changed.

$$x\leq \frac{11}{4}\left(-\frac{10}{7}\right)$$

Multiply \frac{11}{4} times -\frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$x\leq \frac{11\left(-10\right)}{4\times 7}$$

Do the multiplications in the fraction \frac{11\left(-10\right)}{4\times 7}.

$$x\leq \frac{-110}{28}$$

Reduce the fraction \frac{-110}{28} to lowest terms by extracting and canceling out 2.

$$x\leq -\frac{55}{14}$$