Question

name
date
class period
solving absolute value equations coloring activity
directions
solve the
absolute value
equations.
circle your
answer choice
and color the
corresponding
areas in the
picture.
1 (|x - 12| = 24) ((-12, 36)) green
no solution maroon
((-36, 12)) brown
((12, 36)) aqua
2 (|-3x| = 6)
no solution orange
((-2, 2)) lt blue
((-3, 3)) navy
((-2)) silver
3 (|-x - 6| = 8) ((-14, -2)) purple
((2, 14)) brown
no solution white
((-14, 2)) pink
4 (|8 - 4x| = 28) ((-5, 9)) yellow
no solution dk green
((-9, -5)) red
((5, 9)) green
5 (|x + 4| - 5 = 4) ((-13, -5)) silver
((5, 13)) orange
no solution maroon
((-13, 5)) red
6 (4|x + 11| = 44) ((-22, 0)) white
((0, 22)) navy
({0}) yellow
no solution brown
7 (|10 + 10x| + 5 = 125)
no solution lt blue
((-13, -11)) aqua
((-13, 11)) purple
((11, 13)) pink
8 (\frac{|4x - 2|}{3} = -3) (left{\frac{11}{4}
ight}) red
no solution dk green
(left{-\frac{7}{4}
ight}) lt blue
(left(-\frac{7}{4}, \frac{11}{4}
ight)) black
9 (-4|-10 + x| - 7 = -103)
no solution orange
((-34, -14)) yellow
((-14, 34)) navy
((14, 34)) silver
10 (5|x + 1| + 7 = -38) ((-10, 0)) aqua
((-10 - 0)) green
no solution silver
((8, 10)) pink
11 (4|5 + 2x| + 12 = 136) ((-18, -13)) black
((13, 18)) red
no solution lt brown
((-18, 13)) orange
12 (14|x + 14| + 13 = 69)
no solution dk pink
((-18, -10)) brown
((-10, 18)) tan
((-18, 10)) gray
13 (6 + |2x - 11| = 37) ((-21, 10)) dk green
((-10, 21)) aqua
((-21, -10)) pink
no solution lt blue
14 (6 + 8|7x + 14| = 174) ((1, 5)) white
no solution purple
((-5, 1)) maroon
((-5, -1)) yellow

Explanation:

Step1: Solve \(|x - 12| = 24\)

The absolute value equation \(|A| = B\) (where \(B\geq0\)) has solutions \(A = B\) or \(A=-B\). So for \(|x - 12| = 24\), we have two cases:
Case 1: \(x - 12 = 24\), then \(x = 24 + 12 = 36\).
Case 2: \(x - 12=-24\), then \(x=-24 + 12=-12\).
So the solutions are \(x=-12\) or \(x = 36\), which is the interval \((-12,36)\).

Step2: Match the solution to the color

Looking at the options for problem 1, the solution \((-12,36)\) is associated with the color GREEN.

Answer:

For problem 1, the solution is \((-12,36)\) and the corresponding color is GREEN.