Solve 6div30+(x-6)-50leq1/2

$$6 \div 30 + ( x - 6 ) - 50 \leq \frac { 1 } { 2 }$$

Solve for x

$$x\leq \frac{563}{10}$$

Solution Steps

Reduce the fraction \frac{6}{30} to lowest terms by extracting and canceling out 6.

$$\frac{1}{5}+x-6-50\leq \frac{1}{2}$$

Convert 6 to fraction \frac{30}{5}.

$$\frac{1}{5}+x-\frac{30}{5}-50\leq \frac{1}{2}$$

Since \frac{1}{5} and \frac{30}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-30}{5}+x-50\leq \frac{1}{2}$$

Subtract 30 from 1 to get -29.

$$-\frac{29}{5}+x-50\leq \frac{1}{2}$$

Convert 50 to fraction \frac{250}{5}.

$$-\frac{29}{5}+x-\frac{250}{5}\leq \frac{1}{2}$$

Since -\frac{29}{5} and \frac{250}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-29-250}{5}+x\leq \frac{1}{2}$$

Subtract 250 from -29 to get -279.

$$-\frac{279}{5}+x\leq \frac{1}{2}$$

Add \frac{279}{5} to both sides.

$$x\leq \frac{1}{2}+\frac{279}{5}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{279}{5} to fractions with denominator 10.

$$x\leq \frac{5}{10}+\frac{558}{10}$$

Since \frac{5}{10} and \frac{558}{10} have the same denominator, add them by adding their numerators.

$$x\leq \frac{5+558}{10}$$

Add 5 and 558 to get 563.

$$x\leq \frac{563}{10}$$