Assignments:

Unfinished Assignment Study Questions for Lesson 17

Lesson Objectives:

- Solve absolute value equation.
- Solve absolute value inequality.

The absolute value of a number is its distance from 0 on a number line.

So for any positive value a, the abs(x) = a means that x = a or x = -a.

Solve abs(x-1) + 4 = 10.

So start by subtracting 4 from both sides. This gives us abs(x-1) = 6.

So x-1 = 6 or x-1 = -6. So if we add 1 to both sides, we have x = 7 or x = -5.

So let's check x = 7. abs(7-1)+4 = 10. That means 6+4 = 10 or 10 = 10. So, this is a true statement.

Now let's check x = -5. We get abs(-5-1)+4 = 10, which is 6+4 = 10 or 10 = 10. Another true statement.

So the solutions are 7 and -5.

Absolute Value Inequalities.

If a > 0 and abs(x) < a, then -a < x < a.
If a > 0 and abs(x) > a, then x < -a or x > a.
Similarly, if a > 0 and abs(x) <= a, then -a <= x <= a.
And if a > 0 and abs(x) >= a, then x <= -a or x >= a.

Solve and give your solution set in interval notation and then graph the solution set.

abs(x+12) >= 15. This means that x+12 >= 15 or x+12 <= -15. So if we subtract 12 from both sides, we get x >= 3 or if we subtract 12 over here, we get x <= -27.

We can graph the solution set by having a closed circle at -27 and a closed circle at 3. And x <= -27, so we shade to the left, and >= +3, so we shade to the right.

In interval notation, this is (-oo, -27] cup [3, oo).