Basic
What does the absolute value of a number represent?
Distance from 0 on a number line.
Solve ∣x∣ = 6
x = 6, x = -6
{6, -6}
Solve ∣2x∣=10
x=5,−5
Draw the solution set of ∣x–3∣=2
Plot points at x=1 and x=5
A concert ticket normally costs $100, give or take $12.
Write an absolute value equation to model this.
∣x – 100∣ = 12
True or False: ∣−12∣=−12
False, absolute value is always nonnegative.
Solve ∣y – 5∣ = 2
y=3 y=7
{3, 7}
Solve ∣3x–2∣=4
x=2, −2/3
Graph the solution set of ∣y+4∣=3 on a number line.
Plot points at y=−7 and y=−1
A water bottle is labeled 16 oz, but the actual volume can vary by up to 3 oz.
What is the range of possible volumes?
13 oz to 19 oz.
The equation |x -5| = 2 means x is ________ units away from ______.
2 units away from 5
Solve ∣m+4∣=9
m=5 m= -13
{-13, 5}
Solve ∣5 - x∣ = 8
{-3, 13}
You are given a number line with points plotted at x=0 and x=8
Write an absolute value equation that matches this solution set.
∣x–4∣=4
A runner finishes a race in 50 minutes, give or take 2 minutes.
Write and solve an absolute value equation for possible finish times.
∣x–50∣=2 → {48, 52}
What are the two cases for solving ∣a – b∣=c?
a – b = c or a – b = −c
Solve ∣x + 4∣= -2
∅ (no solution)
Solve ∣4x + 3∣ = 9
{-3, 3/2}
Graph the solutions to ∣n–7∣=0
A single point at n=7
A number is 7 units away from 4.
Write and solve an absolute value equation.
∣x–4∣=7 → {−3, 11}
Write an absolute value equation whose solutions are x = -4 and x= 10
∣x - 3∣ = 7
Solve ∣d + 7∣ = 12
d = 5 d = -19
{-19, 5}
Solve ∣x/2 + 1∣=6
{-14, 10}
Graph the solutions to ∣x+3∣=−4 on a number line.
No solution → ∅ (no points to plot)
A box is supposed to weigh 30 lb, but the company reports a tolerance of –4 lb.
Write and solve the absolute value equation.
|x – 30| = –4 → ∅ (no solution, tolerance can’t be negative)