Solve 15x+5left(120-xright)leq13.5+7.5left(120-xright)

$$15x+5 \left( 120-x \right) \leq 13.5+7.5 \left( 120-x \right)$$

Solve for x

$$x\leq \frac{627}{35}$$

Solution Steps

Use the distributive property to multiply 5 by 120-x.

$$15x+600-5x\leq 13.5+7.5\left(120-x\right)$$

Combine 15x and -5x to get 10x.

$$10x+600\leq 13.5+7.5\left(120-x\right)$$

Use the distributive property to multiply 7.5 by 120-x.

$$10x+600\leq 13.5+900-7.5x$$

Add 13.5 and 900 to get 913.5.

$$10x+600\leq 913.5-7.5x$$

Add 7.5x to both sides.

$$10x+600+7.5x\leq 913.5$$

Combine 10x and 7.5x to get 17.5x.

$$17.5x+600\leq 913.5$$

Subtract 600 from both sides.

$$17.5x\leq 913.5-600$$

Subtract 600 from 913.5 to get 313.5.

$$17.5x\leq 313.5$$

Divide both sides by 17.5. Since 17.5 is positive, the inequality direction remains the same.

$$x\leq \frac{313.5}{17.5}$$

Expand \frac{313.5}{17.5} by multiplying both numerator and the denominator by 10.

$$x\leq \frac{3135}{175}$$

Reduce the fraction \frac{3135}{175} to lowest terms by extracting and canceling out 5.

$$x\leq \frac{627}{35}$$