Solve 12(x+5)div31leq4div5

$$12(x+5) \div 31 \leq 4 \div 5$$

Solve for x

$$x\leq -\frac{44}{15}$$

Solution Steps

Multiply both sides by 31. Since 31 is positive, the inequality direction remains the same.

$$12\left(x+5\right)\leq \frac{4}{5}\times 31$$

Use the distributive property to multiply 12 by x+5.

$$12x+60\leq \frac{4}{5}\times 31$$

Express \frac{4}{5}\times 31 as a single fraction.

$$12x+60\leq \frac{4\times 31}{5}$$

Multiply 4 and 31 to get 124.

$$12x+60\leq \frac{124}{5}$$

Subtract 60 from both sides.

$$12x\leq \frac{124}{5}-60$$

Convert 60 to fraction \frac{300}{5}.

$$12x\leq \frac{124}{5}-\frac{300}{5}$$

Since \frac{124}{5} and \frac{300}{5} have the same denominator, subtract them by subtracting their numerators.

$$12x\leq \frac{124-300}{5}$$

Subtract 300 from 124 to get -176.

$$12x\leq -\frac{176}{5}$$

Divide both sides by 12. Since 12 is positive, the inequality direction remains the same.

$$x\leq \frac{-\frac{176}{5}}{12}$$

Express \frac{-\frac{176}{5}}{12} as a single fraction.

$$x\leq \frac{-176}{5\times 12}$$

Multiply 5 and 12 to get 60.

$$x\leq \frac{-176}{60}$$

Reduce the fraction \frac{-176}{60} to lowest terms by extracting and canceling out 4.

$$x\leq -\frac{44}{15}$$