Q: If $$|2x - 5| \u003c 9$$ models the safe temperature range (in $$^C) $$for a chemical reaction, what is the maximum and minimum temperature allowed?

Minimum: $$-2^C$$, Maximum: $$7^C$$

Question 1

Given the absolute value inequality $$|2x - 5| \u003c 9$$, which of the following is the correct way to rewrite the inequality without absolute value bars?

Accepted Answer

$$-9 \u003c 2x - 5 \u003c 9$$

Question 2

Solve the inequality $$|2x - 5| \u003c 9$$ and express the solution set in interval notation.

Accepted Answer

$$(-2, 7)$$

Question 3

Which of the following represents the solution set for $$|2x - 5| \u003c 9 on a $$number line?

Accepted Answer

A shaded region between $$x = -2$$ and $$x = 7$$, not including endpoints

Question 4

If $$|2x - 5| \u003c 9$$ models the safe temperature range (in $$^C) $$for a chemical reaction, what is the maximum and minimum temperature allowed?

Accepted Answer

Minimum: $$-2^C$$, Maximum: $$7^C$$

Question 5

Which of the following is the correct approach to solve $$|ax + b| \u003c c$$ for $$x$$?

Accepted Answer

$$-c \u003c ax + b \u003c c$$

Question 6

Suppose $$|2x - 5| \u003c 9$$ represents the acceptable deviation from a target value in a manufacturing process. If the target is $$x = 5$$, what is the range of acceptable $$x$$ values?

Accepted Answer

$$x 	ext{ must be between } -2 	ext{ and } 7$$

Question 7

Which of the following is a common mistake when solving $$|2x - 5| \u003c 9$$?

Accepted Answer

Solving only $$2x - 5  -9$$

Question 8

If $$|2x - 5| \u003c 9$$ and $$x$$ must be an integer, how many integer solutions are there?

Accepted Answer

10

Question 9

Which interval notation correctly represents all $$x$$ values that satisfy $$|2x - 5| \u003c 9$$?

Accepted Answer

$$(-2, 7)$$

Question 10

A student claims the solution to $$|2x - 5| \u003c 9 is$$ $$x \u003c 7. $$Which error did the student make?

Accepted Answer

They only considered the upper bound and ignored the lower bound.

Question 11

If $$|2x - 5| \u003c 9$$ describes the acceptable error in a medical dosage calculation, what is the total width of the interval of acceptable $$x$$ values?

Accepted Answer

Question 12

If the solution to $$|2x - 5| \u003c 9 is$$ $$x 	ext{ in } (-2, 7)$$, what is the midpoint of this interval?

Accepted Answer

Solving Absolute Value Inequalities in Precalculus

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