Solve 1/3+1/2xleq5/6*2/3

$$\frac { 1 } { 3 } + \frac { 1 } { 2 } x \leq \frac { 5 } { 6 } \times \frac { 2 } { 3 }$$

Solve for x

$$x\leq \frac{4}{9}$$

Solution Steps

Multiply \frac{5}{6} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}+\frac{1}{2}x\leq \frac{5\times 2}{6\times 3}$$

Do the multiplications in the fraction \frac{5\times 2}{6\times 3}.

$$\frac{1}{3}+\frac{1}{2}x\leq \frac{10}{18}$$

Reduce the fraction \frac{10}{18} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}+\frac{1}{2}x\leq \frac{5}{9}$$

Subtract \frac{1}{3} from both sides.

$$\frac{1}{2}x\leq \frac{5}{9}-\frac{1}{3}$$

Least common multiple of 9 and 3 is 9. Convert \frac{5}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{1}{2}x\leq \frac{5}{9}-\frac{3}{9}$$

Since \frac{5}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x\leq \frac{5-3}{9}$$

Subtract 3 from 5 to get 2.

$$\frac{1}{2}x\leq \frac{2}{9}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}. Since \frac{1}{2} is positive, the inequality direction remains the same.

$$x\leq \frac{2}{9}\times 2$$

Express \frac{2}{9}\times 2 as a single fraction.

$$x\leq \frac{2\times 2}{9}$$

Multiply 2 and 2 to get 4.

$$x\leq \frac{4}{9}$$