Solve for w and graph the solution.
45=|
–
9w+45|
Click to select points on the number line.



The equation is given as:

\[
45 = | -9w + 45 |
\]

To solve this absolute value equation, follow these steps:

### Step 1: Remove the absolute value
Recall that \( | x | = a \) implies two cases:
1. \( x = a \)
2. \( x = -a \)

Thus, we have:

1. \( -9w + 45 = 45 \)
2. \( -9w + 45 = -45 \)

### Step 2: Solve each case

#### Case 1: \( -9w + 45 = 45 \)

\[
-9w = 45 - 45 = 0
\]

\[
w = \frac{0}{-9} = 0
\]

#### Case 2: \( -9w + 45 = -45 \)

\[
-9w = -45 - 45 = -90
\]

\[
w = \frac{-90}{-9} = 10
\]

### Step 3: Solutions
The two solutions are \( w = 0 \) and \( w = 10 \).

### Graphing the solutions
We can graph the solutions on a number line, with points at \( w = 0 \) and \( w = 10 \).

Would you like a graph of this solution? 

#### Here are 5 related questions for further practice:
1. Solve \( |3x + 5| = 11 \).
2. Solve \( |7 - 2y| = 3 \).
3. Solve \( 2|x - 4| = 8 \).
4. Solve \( |5z + 1| = 0 \).
5. Solve \( |x + 7| = 10 \).

**Tip**: When solving absolute value equations, always remember to consider both the positive and negative cases!

Solve for w and graph the solution.
45=| -9w+45 |

Discover how to solve the absolute value equation 45 = | -9w + 45 | step by step. This guide covers solving algebraic absolute value equations and graphing the solution on a number line. Perfect for students in Grades 8-10.

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