2.7 Notes Alg1.notebook
October 11, 2012
2­7 Solving Absolute Value Inequalities
Skills we've learned
1) The target heart rate during exercise for a 15 year­old is between 154 and 174 beats per minute inclusive. Write a compound inequality to show the heart rates that are within the target range. Graph the solutions. Solve each compound inequality and graph the solutions.
3) 3 + r > −2 OR 3 + r < −7 2) 2 ≤ 2w + 4 ≤ 12
Write the compound inequality shown by the graph.
4)
5)
Skills we need
3)
2)
1)
Warm­up Answers
1) The target heart rate during exercise for a 15 year­old is between 154 and 174 beats per minute inclusive. Write a compound inequality to show the heart rates that are within the target range. Graph the solutions. Solve each compound inequality and graph the solutions.
2) 2 ≤ 2w + 4 ≤ 12
3) 3 + r > −2 OR 3 + r < −7 Write the compound inequality shown by the graph.
4)
5)
−2 ≤ a < 4 x < −7 OR x ≥ 0
1)
2)
3)
2.7 Notes Alg1.notebook
October 11, 2012
2­7 Solving Absolute Value Inequalities
Solve inequalities in one variable involving absolute­value expressions.
You can solve an absolute value inequality to determine the safe range for the pressure of a fire extinguisher.
2.7 Notes Alg1.notebook
October 11, 2012
I. Solving Absolute Value Inequalities with Less Than
1. Solve the inequality and graph the solutions.
A) |x| ­ 3 < ­1
2) 2|x| < 6
B) |x ­ 1| < 2
3) |x + 3| ­ 4.5 < 7.5
2.7 Notes Alg1.notebook
October 11, 2012
II. Solving Absolute Value Inequalities
with Greater Than
4. Solve the inequality and graph the solutions.
A) |x| + 14 > 19
B) 3 + |x + 2 |> 5
2.7 Notes Alg1.notebook
October 11, 2012
5)
6)
III. Applications
A pediatrician recommends that a baby’s bath water be 95°F, but it is acceptable for the temperature to vary from this amount by as much as 3°F. Write and solve an absolute­
value inequality to find the range of acceptable temperatures. Graph the solutions.
The difference between t and the ideal temperature is at most 3°F.
2.7 Notes Alg1.notebook
7)
October 11, 2012
A dry­chemical fire extinguisher should be pressurized to 125 psi, but it is acceptable for the pressure to differ from this value by at most 75 psi. Write and solve an absolute­value inequality to find the range of acceptable pressures. Graph the solution. The difference between t and the ideal temperature is at most 3°F.
IV. Special Cases of Absolute Value
When solving an absolute­value inequality, you may get a statement that is true for all values of the variable. In this case, all real numbers are solutions of the original inequality. If you get a false statement when solving an absolute­value inequality, the original inequality has no solutions. try substituting x­values in the equation to check your answer.
2.7 Notes Alg1.notebook
8) |x| ­ 9 > ­11
October 11, 2012
9) 4|x ­ 3.5| < ­8 2.7 p. 145 #1 ­ 4, 8, 9, 11 ­ 15, 21 ­ 27 (x3), 32 ­ 34, 39 ­ 51 odd, 56 ­ 59 *28 problems