Solve x:1/5-1geq2/3

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

Solve for x

$$x\geq \frac{1}{3}$$

Solution Steps

Add 1 to both sides.

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

Convert 1 to fraction \frac{3}{3}.

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

Since \frac{2}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

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

Add 2 and 3 to get 5.

$$\frac{x}{\frac{1}{5}}\geq \frac{5}{3}$$

Multiply both sides by \frac{1}{5}. Since \frac{1}{5} is positive, the inequality direction remains the same.

$$x\geq \frac{5}{3}\times \frac{1}{5}$$

Multiply \frac{5}{3} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$x\geq \frac{5\times 1}{3\times 5}$$

Cancel out 5 in both numerator and denominator.

$$x\geq \frac{1}{3}$$