Questions: Amber is solving the inequality x+6-12<13 by graphing. Which equations should Amber graph? y1=x+6, y2=25 y1=x+6 y2=25 y1=x+6, y2=13 y1=x+6, y2=13

Transcript text: Amber is solving the inequality $|x+6|-12<13$ by graphing. Which equations should Amber graph? $y_{1}=|x+6|, y_{2}=25$ $y_{1}=x+6 y_{2}=25$ $y_{1}=|x+6|, y_{2}=13$ $y_{1}=x+6, y_{2}=13$

Solution

Solution Steps

To solve the inequality $|x+6|-12<13$, we first simplify it to $|x+6| < 25$. This means we need to graph the absolute value function $y_1 = |x+6|$ and the constant function $y_2 = 25$. The solution to the inequality will be the x-values where the graph of $y_1$ is below the graph of $y_2$.

Step 1: Understand the Inequality

The given inequality is:

\[ |x+6| - 12 < 13 \]

To solve this inequality, we first isolate the absolute value expression.

Step 2: Isolate the Absolute Value

Add 12 to both sides of the inequality:

\[ |x+6| - 12 + 12 < 13 + 12 \]

This simplifies to:

\[ |x+6| < 25 \]

Step 3: Determine the Graphing Equations

Amber needs to graph the absolute value inequality. To do this, she should graph the absolute value function and the constant on the right side of the inequality. Therefore, the equations to graph are: