Question

Solve the following inequality algebraically. 2 |x + 1| +1 < 19Absolute value inequalities

Answer 1

2|x + 1| + 1 < 19

1 is adding on the left, then it will subtract on the right

2|x + 1| < 19 - 1

2|x + 1| < 18

2 is multiplying on the left, then it will divide on the right

|x + 1| < 18/2

|x + 1| < 9

Now, we have two options:

x + 1 < 9 or x + 1 > -9

x < 9 - 1 x > -9 - 1

x < 8 x > -10

Then, the solution is -10 < x < 8