Solve 2/3x-10>7/6

$$\frac { 2 } { 3 } x - 10 > \frac { 7 } { 6 }$$

Solve for x

$$x>\frac{67}{4}$$

Solution Steps

Add 10 to both sides.

$$\frac{2}{3}x>\frac{7}{6}+10$$

Convert 10 to fraction \frac{60}{6}.

$$\frac{2}{3}x>\frac{7}{6}+\frac{60}{6}$$

Since \frac{7}{6} and \frac{60}{6} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}x>\frac{7+60}{6}$$

Add 7 and 60 to get 67.

$$\frac{2}{3}x>\frac{67}{6}$$

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}. Since \frac{2}{3} is positive, the inequality direction remains the same.

$$x>\frac{67}{6}\times \frac{3}{2}$$

Multiply \frac{67}{6} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{67\times 3}{6\times 2}$$

Do the multiplications in the fraction \frac{67\times 3}{6\times 2}.

$$x>\frac{201}{12}$$

Reduce the fraction \frac{201}{12} to lowest terms by extracting and canceling out 3.

$$x>\frac{67}{4}$$