Solve 3a+2.5(2600-a)leq7000

$$3 a + 2.5 ( 2600 - a ) \leq 7000$$

Solve for a

$$a\leq 1000$$

Solution Steps

Use the distributive property to multiply 2.5 by 2600-a.

$$3a+6500-2.5a\leq 7000$$

Combine 3a and -2.5a to get 0.5a.

$$0.5a+6500\leq 7000$$

Subtract 6500 from both sides.

$$0.5a\leq 7000-6500$$

Subtract 6500 from 7000 to get 500.

$$0.5a\leq 500$$

Divide both sides by 0.5. Since 0.5 is positive, the inequality direction remains the same.

$$a\leq \frac{500}{0.5}$$

Expand \frac{500}{0.5} by multiplying both numerator and the denominator by 10.

$$a\leq \frac{5000}{5}$$

Divide 5000 by 5 to get 1000.

$$a\leq 1000$$