Solve 180x+240left(2/3x-5right)leq21300

$$180x+240 \left( \frac{ 2 }{ 3 } x-5 \right) \leq 21300$$

Solve for x

$$x\leq \frac{1125}{17}$$

Solution Steps

Use the distributive property to multiply 240 by \frac{2}{3}x-5.

$$180x+240\times \frac{2}{3}x-1200\leq 21300$$

Express 240\times \frac{2}{3} as a single fraction.

$$180x+\frac{240\times 2}{3}x-1200\leq 21300$$

Multiply 240 and 2 to get 480.

$$180x+\frac{480}{3}x-1200\leq 21300$$

Divide 480 by 3 to get 160.

$$180x+160x-1200\leq 21300$$

Combine 180x and 160x to get 340x.

$$340x-1200\leq 21300$$

Add 1200 to both sides.

$$340x\leq 21300+1200$$

Add 21300 and 1200 to get 22500.

$$340x\leq 22500$$

Divide both sides by 340. Since 340 is positive, the inequality direction remains the same.

$$x\leq \frac{22500}{340}$$

Reduce the fraction \frac{22500}{340} to lowest terms by extracting and canceling out 20.

$$x\leq \frac{1125}{17}$$