solve and check 5b+2|+3<12

Question

solve |5b+2|+3<12.

Answer 1

Remember the formula |x | < a  ⇒-a  < x  < a

|5b + 2| +3 < 12

-12 < 5b + 2 +3 < 12

-12 < 5b + 5 < 12

-12 - 5 < 5b + 5 - 5 < 12 - 5

-17 < 5b  < 7

-17/5 < 5b /5 < 7/5

-3.4 < b  < 1.4

Check

|5b + 2| + 3 < 12

If b = 1

|5(1) + 2| + 3 < 12

7 + 3 < 12

10 < 12

Above statement is true.

Comments

please check your answer.

Answer 2

The inequality is .

Subtract 3 from each side.

The absolute value inequality  is equivalent to .

Solve the inequality for b.

Subtract 2 from each part.

Divide each part by 5.

.

To check the solution, let the value of in the original inequality.

The above statement is true, so the value of is the solution of inequality.

The solution set is .