AFDA – Unit 3: Absolute Value + Piecewise Functions
Day 2 Notes: Absolute Value Inequalities
Name: _________________
Block: _____ Date:_______
Today you will learn…
 how to solve and graph one variable absolute value inequalities
 what to do when you have a special case of absolute value inequalities
Absolute Value Inequalities
Conjunctions: _______________
Disjunctions:______________
If |𝑥| ≤ 4, what are the possible values of 𝑥?
If |𝑥| ≥ 4, what are the possible values of 𝑥?
When solving absolute value inequalities…
 Get rid of any “guards” with reverse PEMDAS
 Once the guards are gone, rewrite as two separate inequalities.
o Flip the inequality sign and change the numerical sign.
 Solve each equation for the variable
Solve and graph the inequalities.
1. |2𝑥 − 3| < 3
2. |3𝑥 + 5| ≥ 10
3. 9 − |3 − 𝑚| ≥ 1
𝑥
5. −2 | − 9| ≤ 12
4
1
4. 11 + |4𝑥 − 1| > 13
2
6. |2𝑥 + 3| + 9 ≤ 7
Special Cases:
Can an absolute value ever be negative? ______________
Therefore, the answer x  2   1 must be _________________.
How about x  3   5 ? It will _______________ be greater than a negative
number.
Therefore, the answer must be _________________________.
Solve these special cases:
1.
| x  7 | 5
2.
| x  30 | 50
3.
2 | x  3 | 10
4.
3 | x  25 | 60
Word Problems:
1. The ideal diameter of a piston for one particular type of car is 88 mm. The actual
diameter can vary from the ideal by at most .008 mm. Write an absolute value
inequality and then find the range of acceptable diameters for the piston.
2. The ideal weight of one type of clock is 33.86 ounces. The actual weight can
vary from the ideal by .05 ounces. Write an absolute value inequality. What is
the range of acceptable weights for the clock?
3. A carpenter is using a lathe to make legs for a table. In order for the leg to fit, it
needs to be 150 mm wide, allowing for a margin of error of 2.5 mm. Write an
absolute value inequality and then find the range of widths the table leg can be.
4. Before the start of professional soccer games, the balls must be inflated to a
pressure of 13 psi with an absolute error of .05 psi. Write an absolute value
inequality and then find the minimum and maximum pressures for the soccer
balls.