Solve for

w

and graph the solution.

|

3

w

–

675

|

=

225

Click to select points on the number line.

-

150

,

-

100

,

-

50

,

0

,

50

,

100

,

150

,

200

,

250

,

300

,

350

,

400

,

450

,

tick mark,

Submit

We start with the equation:

\[
|3w - 675| = 225
\]

### Step 1: Solve the absolute value equation
An absolute value equation like this has two cases to consider:

1. \(3w - 675 = 225\)
2. \(3w - 675 = -225\)

#### Case 1: \(3w - 675 = 225\)
\[
3w = 225 + 675
\]
\[
3w = 900
\]
\[
w = \frac{900}{3} = 300
\]

#### Case 2: \(3w - 675 = -225\)
\[
3w = -225 + 675
\]
\[
3w = 450
\]
\[
w = \frac{450}{3} = 150
\]

### Step 2: Solutions
The solutions to the equation are:
\[
w = 300 \quad \text{and} \quad w = 150
\]

### Step 3: Graph the solution
Now, let's mark these points on the number line. The two solutions are \(w = 150\) and \(w = 300\), which lie between the given tick marks:

- \(

Solve for w and graph the solution: |3w - 675| = 225. Click to select points on the number line: -150, -100, -50, 0, 50, 100, 150, 200, 250, 300, 350, 400, 450.

Learn how to solve the absolute value equation |3w - 675| = 225 with a detailed step-by-step process. This problem explores algebraic concepts like absolute value equations and linear equation solving. The solution includes marking points on the number line at w = 150 and w = 300. Suitable for students in Grades 8-10.

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