Taming the modulus

Mathematics · Algebra · ages 16-17

Name ______________________ Date ____________

|x - 2| = 5. What is the larger solution?
Answer: ______________
Where does y = |x - 3| turn?
- x = 3
- x = 0
- x = -3
- x = 1
Where does the V for x minus 3 bend?
- x = 3
- x = 0
- x = minus 3
The graph for x minus 3 is a V with low tip at (3, 0).
Circle one: True False
|x + 4| = 9. What is the larger solution?
Answer: ______________
What solves bars round x minus 1 under 4?
- minus 3 through 5
- x under 5
- 1 through 4
What are the solutions of |2x - 4| = 6?
- 5 and 1
- 3 and -3
- 5 only
- 5 and -1
Maya says |x - 2| > 5 means x > 7 or x < -3. Is Maya right?
Circle one: True False
Keep just roots that pass: bars round x set to x plus 2.
- 1 only
- minus 1 only
- minus 1 and 1
|2x + 1| = 11. What is the larger solution?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

7 · x - 2 = 5 gives 7; the other case gives -3.
x = 3 · Inside zero: x - 3 = 0 gives 3. The -3 option flips the sign.
x = 3 · Inner zero: x minus 3 as 0 gives 3.
True · Each arm runs as a straight ray from that tip.
5 · x + 4 = 9 gives 5; the other gives -13.
minus 3 through 5 · Within 4 of 1 runs from minus 3 to 5.
5 and -1 · 2x - 4 = 6 gives 5; 2x - 4 = -6 gives -1. The 5 only option drops a case.
True · Beyond 5 from 2 in either direction, joined by OR.
minus 1 only · 1 breaks the check (1 versus 3); minus 1 holds.
5 · 2x + 1 = 11 gives 5; the other gives -6.