Solve 5(1/2x+3)leq4(1/3x+5)

$$5 ( \frac { 1 } { 2 } x + 3 ) \leq 4 ( \frac { 1 } { 3 } x + 5 )$$

Solve for x

$$x\leq \frac{30}{7}$$

Solution Steps

Use the distributive property to multiply 5 by \frac{1}{2}x+3.

$$5\times \frac{1}{2}x+15\leq 4\left(\frac{1}{3}x+5\right)$$

Multiply 5 and \frac{1}{2} to get \frac{5}{2}.

$$\frac{5}{2}x+15\leq 4\left(\frac{1}{3}x+5\right)$$

Use the distributive property to multiply 4 by \frac{1}{3}x+5.

$$\frac{5}{2}x+15\leq 4\times \frac{1}{3}x+20$$

Multiply 4 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{5}{2}x+15\leq \frac{4}{3}x+20$$

Subtract \frac{4}{3}x from both sides.

$$\frac{5}{2}x+15-\frac{4}{3}x\leq 20$$

Combine \frac{5}{2}x and -\frac{4}{3}x to get \frac{7}{6}x.

$$\frac{7}{6}x+15\leq 20$$

Subtract 15 from both sides.

$$\frac{7}{6}x\leq 20-15$$

Subtract 15 from 20 to get 5.

$$\frac{7}{6}x\leq 5$$

Multiply both sides by \frac{6}{7}, the reciprocal of \frac{7}{6}. Since \frac{7}{6} is positive, the inequality direction remains the same.

$$x\leq 5\times \frac{6}{7}$$

Express 5\times \frac{6}{7} as a single fraction.

$$x\leq \frac{5\times 6}{7}$$

Multiply 5 and 6 to get 30.

$$x\leq \frac{30}{7}$$