Lesson 5: 5-5 Solving Inequalities involving Absolute Value

How is solving an Ineqaulity involving an absolute value similar to solving an equation involving an absolute value?

Is it possible for an absolute value expression to be less than or equal to a negative constant?

A.CED.1 Creat equations and inequalities in one variable and use them to solve problems.

A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

SAT questions related to inequalities: 5-4-13,7-4-5,4-4-19,8-3-6,1-4-28,5-3-7,6-3-14;

Absolute value inequalities can be solved algebraically by writing them as compound inequalities. When compound absolute value inequalities are being solved, there are two cases to consider: the expression inside the absolute value symbol is positive or 0, and the expression inside the absolute value symbol is negative.

Some companies use absolute value inequalities to control the quality of their product. To make baby carrots, long carrots are sliced into 3-inch sections and peeled. If the machine is accurate to within 1/8 of an inch, the lenght ranges from 2 7/8 inches to 3 1/8 inches.

If students do not understnad why l m+2 l < 11 is rewritten as m+2 <11 and m+2 > -11 then have them rewrite the second inequality as -(m+2)<11 and multiply each side by -1 to yield m+2>-11. This method makes the switch of the direction of the inequality more obvious, as students must make the switch when they multpily each side by -1.

Practice: Exercises 1 - 7

Exercises 48-55

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