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2.7 Notes Alg1.notebook October 11, 2012 Skills we've learned Skills we need 1) 2) 3) 27 Solving Absolute Value Inequalities 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) 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) x < −7 OR x ≥0 2≤ a< 4 1) 2) 3)

# 27 Solving Absolute Value Inequalities · 2.7 Notes Alg1.notebook October 11, 2012 27 Solving Absolute Value Inequalities Solve inequalities in one variable involving absolutevalue

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### Text of 27 Solving Absolute Value Inequalities · 2.7 Notes Alg1.notebook October 11, 2012 27 Solving...

2.7 Notes Alg1.notebook October 11, 2012

Skills we've learned

Skills we need1) 2) 3)

2­7 Solving Absolute Value Inequalities

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)

Warm­up Answers1) 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)

x < −7  OR  x ≥ 0 −2 ≤ a < 4

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

A) |x| ­ 3 < ­1 B) |x ­ 1| < 2

1.  Solve the inequality and graph the solutions.

2)  2|x| < 6 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

6)5)

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 absolute­value inequality to find the range of acceptable temperatures. Graph the solutions.

III.  Applications

The difference between t and the ideal temperature is at most 3°F.

2.7 Notes Alg1.notebook 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.

7)

IV.  Special Cases of Absolute ValueWhen 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 October 11, 2012

8) |x| ­ 9 > ­11 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

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