Solve 2(3+5a)leq5(4+a)

$$2 ( 3 + 5 a ) \leq 5 ( 4 + a )$$

Solve for a

$$a\leq \frac{14}{5}$$

Solution Steps

Use the distributive property to multiply 2 by 3+5a.

$$6+10a\leq 5\left(4+a\right)$$

Use the distributive property to multiply 5 by 4+a.

$$6+10a\leq 20+5a$$

Subtract 5a from both sides.

$$6+10a-5a\leq 20$$

Combine 10a and -5a to get 5a.

$$6+5a\leq 20$$

Subtract 6 from both sides.

$$5a\leq 20-6$$

Subtract 6 from 20 to get 14.

$$5a\leq 14$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$a\leq \frac{14}{5}$$