Solve 3a+5/2(2600-a)leq7000

$$3 a + \frac { 5 } { 2 } ( 2600 - a ) \leq 7000$$

Solve for a

$$a\leq 1000$$

Solution Steps

Use the distributive property to multiply \frac{5}{2} by 2600-a.

$$3a+\frac{5}{2}\times 2600+\frac{5}{2}\left(-1\right)a\leq 7000$$

Express \frac{5}{2}\times 2600 as a single fraction.

$$3a+\frac{5\times 2600}{2}+\frac{5}{2}\left(-1\right)a\leq 7000$$

Multiply 5 and 2600 to get 13000.

$$3a+\frac{13000}{2}+\frac{5}{2}\left(-1\right)a\leq 7000$$

Divide 13000 by 2 to get 6500.

$$3a+6500+\frac{5}{2}\left(-1\right)a\leq 7000$$

Multiply \frac{5}{2} and -1 to get -\frac{5}{2}.

$$3a+6500-\frac{5}{2}a\leq 7000$$

Combine 3a and -\frac{5}{2}a to get \frac{1}{2}a.

$$\frac{1}{2}a+6500\leq 7000$$

Subtract 6500 from both sides.

$$\frac{1}{2}a\leq 7000-6500$$

Subtract 6500 from 7000 to get 500.

$$\frac{1}{2}a\leq 500$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}. Since \frac{1}{2} is positive, the inequality direction remains the same.

$$a\leq 500\times 2$$

Multiply 500 and 2 to get 1000.

$$a\leq 1000$$