Absolute Value Relationships

Question 5 • TOL-202627-S1-MTH-Algebra 2A - Parker, Carla

Which statements verify that the solution set to |x + 3| < 5 is –8 < x < 2? Check all that apply.

Answer

Substituting a value into the inequality from the solution set, such as –2, will create a true statement.

Substituting a value into the inequality from the solution set, such as 1, will create a false statement.

Substituting a value into the inequality not from the solution set, such as 4, will create a true statement.

Substituting a value into the inequality not from the solution set, such as 6, will create a false statement.

Substituting any value into the inequality will create a true statement.

Explanation

The interval −8 < x < 2 contains values such as −2. Substituting −2 into the original inequality gives |−2 + 3| < 5, or 1 < 5, which is true, so A verifies the solution set. The value 6 is outside the interval, and |6 + 3| < 5 becomes 9 < 5, which is false, so D also verifies it.

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