QuestionMultiple Choice 1 point
4. Coach Brinkman is trying to solve the equation $|x+2|-3=-|x-3|+8$ by graphing. He graphed the right side of the equation and then decided his students needed to do the rest.
Graph the left side of the equation and then state the solution set. $x=-6$ and $x=5$ $x=-1$ and $x=3$ No Solution $x=-5$ and $x=6$

Studdy Solution

STEP 1

1. We are given the equation $|x+2|-3=-|x-3|+8$ .
2. We need to graph the left side of the equation.
3. We need to find the solution set by comparing the graphs of both sides of the equation.

STEP 2

1. Understand the components of the equation.
2. Graph the left side of the equation.
3. Compare the graphs to find the solution set.

STEP 3

Understand the components of the equation. The equation is $|x+2|-3=-|x-3|+8$ .
- The left side is $|x+2|-3$ . - The right side is $-|x-3|+8$ .

STEP 4

Graph the left side of the equation $|x+2|-3$ .
- The graph of $|x+2|$ is a V-shaped graph with a vertex at $x = -2$ . - Subtracting 3 from $|x+2|$ shifts the entire graph downward by 3 units.

STEP 5

Compare the graphs to find the solution set.
- The solution set is where the graphs of the left side and right side intersect.
- By graphing both sides, we find the points of intersection.
- The given options are: - $x = -6$ and $x = 5$ - $x = -1$ and $x = 3$ - No Solution - $x = -5$ and $x = 6$
- After graphing, we see that the graphs intersect at $x = -1$ and $x = 3$ .
The solution set is $x = -1$ and $x = 3$ .

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