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Amber is solving the inequality [tex]\(|x+6| - 12 \ \textless \ 13\)[/tex] by graphing. Which equations should Amber graph?

A. [tex]\(y_1 = |x+6|, y_2 = 25\)[/tex]
B. [tex]\(y_1 = x+6, y_2 = 25\)[/tex]
C. [tex]\(y_1 = |x+6|, y_2 = 13\)[/tex]
D. [tex]\(y_1 = x+6, y_2 = 13\)[/tex]

Sagot :

GinnyAnswer
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]
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