Solve 7(n+14)-5<12n+3

$$7 ( n + 14 ) - 5 < 12 n + 3$$

Solve for n

$$n>18$$

Solution Steps

Use the distributive property to multiply 7 by n+14.

$$7n+98-5<12n+3$$

Subtract 5 from 98 to get 93.

$$7n+93<12n+3$$

Subtract 12n from both sides.

$$7n+93-12n<3$$

Combine 7n and -12n to get -5n.

$$-5n+93<3$$

Subtract 93 from both sides.

$$-5n<3-93$$

Subtract 93 from 3 to get -90.

$$-5n<-90$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$n>\frac{-90}{-5}$$

Divide -90 by -5 to get 18.

$$n>18$$