1. Solving Absolute Value and Radical Equations

2. Absolute Value Equations
Steps
To solve 𝑎𝑥+𝑏 =𝑐:
When 𝑐≥0: solve the linear equations 𝑎𝑥+𝑏=𝑐 and 𝑎𝑥+𝑏=−𝑐
When 𝑐<0: the equation has no solutions. Because absolute value always indicates a number that is not negative.

3. Absolute Value Equations
Examples
1. 𝑥−4 =6

4. Absolute Value Equations
Examples
2. 𝑥−1 =4

5. Absolute Value Equations
Examples
3. 3𝑥+1 =−5

6. Absolute Value Equations
Examples
Sometimes, you will need to isolate the absolute value expression first…
4. 3𝑥+9 −10=−4

7. Absolute Value Equations
Examples
5. −2 5𝑥−1 −3=−11

8. Absolute Value Equations
Examples
You will always need to check your solutions…
6. 𝑥+1 =11𝑥+2

9. Absolute Value Equations
Examples
You will always need to check your solutions…
7. 𝑥−1 =14𝑥+4

10. So, in summary, to solve an absolute value equation…
Isolate the absolute value expression.
Solve two equations.
Check both solutions.

11. Radical Equations
Steps
Isolate the radical expression.
Square or cube both sides (depending on equation).
Solve.
Check your solutions.

12. Radical Equations
Examples
𝑥+1 =4

13. Radical Equations
Examples
𝑥−9 −1=2

14. Radical Equations
Examples
3. 𝑥+1= 7𝑥+15

15. Radical Equations
Examples
𝑥 =10

16. Radical Equations
Examples
𝑥−3 − 𝑥+12 =0