Solve 15x+5(300-x)leq13.5+7.5(300-x)

$$15x+5(300-x) \leq 13.5+7.5(300-x)$$

Solve for x

$$x\leq \frac{1527}{35}$$

Solution Steps

Use the distributive property to multiply 5 by 300-x.

$$15x+1500-5x\leq 13.5+7.5\left(300-x\right)$$

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

$$10x+1500\leq 13.5+7.5\left(300-x\right)$$

Use the distributive property to multiply 7.5 by 300-x.

$$10x+1500\leq 13.5+2250-7.5x$$

Add 13.5 and 2250 to get 2263.5.

$$10x+1500\leq 2263.5-7.5x$$

Add 7.5x to both sides.

$$10x+1500+7.5x\leq 2263.5$$

Combine 10x and 7.5x to get 17.5x.

$$17.5x+1500\leq 2263.5$$

Subtract 1500 from both sides.

$$17.5x\leq 2263.5-1500$$

Subtract 1500 from 2263.5 to get 763.5.

$$17.5x\leq 763.5$$

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

$$x\leq \frac{763.5}{17.5}$$

Expand \frac{763.5}{17.5} by multiplying both numerator and the denominator by 10.

$$x\leq \frac{7635}{175}$$

Reduce the fraction \frac{7635}{175} to lowest terms by extracting and canceling out 5.

$$x\leq \frac{1527}{35}$$