Solve 180x+240(2/3x-5)leq2130

$$180 x + 240 ( \frac { 2 } { 3 } x - 5 ) \leq 2130$$

Solve for x

$$x\leq \frac{333}{34}$$

Solution Steps

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

$$180x+240\times \frac{2}{3}x-1200\leq 2130$$

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

$$180x+\frac{240\times 2}{3}x-1200\leq 2130$$

Multiply 240 and 2 to get 480.

$$180x+\frac{480}{3}x-1200\leq 2130$$

Divide 480 by 3 to get 160.

$$180x+160x-1200\leq 2130$$

Combine 180x and 160x to get 340x.

$$340x-1200\leq 2130$$

Add 1200 to both sides.

$$340x\leq 2130+1200$$

Add 2130 and 1200 to get 3330.

$$340x\leq 3330$$

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

$$x\leq \frac{3330}{340}$$

Reduce the fraction \frac{3330}{340} to lowest terms by extracting and canceling out 10.

$$x\leq \frac{333}{34}$$