To solve the inequality [tex]\( |x+6| - 12 < 13 \)[/tex] by graphing, Amber needs to follow these steps:
1. First, simplify the inequality:
[tex]\( |x+6| - 12 < 13 \)[/tex]
Add 12 to both sides to isolate the absolute value expression:
[tex]\( |x+6| - 12 + 12 < 13 + 12 \)[/tex]
Simplifies to:
[tex]\( |x+6| < 25 \)[/tex]
2. Next, identify the key components to graph:
To convert this inequality into a graphical form, Amber needs to consider the following:
- The absolute value function [tex]\( y_1 = |x + 6| \)[/tex].
- The constant value [tex]\( y_2 = 25 \)[/tex].
3. Graph the equations:
Therefore, the equations Amber should graph are:
[tex]\[
y_1 = |x + 6|
\][/tex]
[tex]\[
y_2 = 25
\][/tex]
By graphing these two equations, Amber can visually interpret the region where [tex]\( |x + 6| < 25 \)[/tex].
Thus, the correct answer is:
[tex]\[ y_1 = |x + 6|, y_2 = 25 \][/tex]
