https://file.aiquickdraw.com/mathbot/file/1726715178995gb927exi.jpg

The equation shown in the image is:

\[
2 + |9x + 3| = 23
\]

To solve this, we proceed with the following steps:

### Step 1: Isolate the absolute value expression
First, subtract 2 from both sides to isolate the absolute value:

\[
|9x + 3| = 23 - 2
\]

\[
|9x + 3| = 21
\]

### Step 2: Solve for the two cases
Since this is an absolute value equation, we have two cases to consider:

1. \(9x + 3 = 21\)
2. \(9x + 3 = -21\)

#### Case 1: \(9x + 3 = 21\)
Solve for \(x\):

\[
9x = 21 - 3
\]
\[
9x = 18
\]
\[
x = \frac{18}{9} = 2
\]

#### Case 2: \(9x + 3 = -21\)
Solve for \(x\):

\[
9x = -21 - 3
\]
\[
9x = -24
\]
\[
x = \frac{-24}{9} = -\frac{8}{3}
\]

### Step 3: Final solutions
The two solutions to the equation are:

\[
x = 2 \quad \text{or} \quad x = -\frac{8}{3}
\]

Would you like more details on any step, or do you have any questions?

### Related Questions:
1. How do you handle equations without absolute value?
2. What is the significance of absolute values in equations?
3. Can you explain why absolute value creates two cases?
4. How would you solve if there were additional terms on both sides of the equation?
5. How can you verify your solution by plugging it back into the equation?

### Tip:
Always remember to check both cases of an absolute value equation by plugging the solutions back into the original equation to ensure they satisfy the condition.

Learn how to solve the absolute value equation 2 + |9x + 3| = 23 step-by-step. This problem covers algebraic concepts like absolute value properties and solving linear equations. Ideal for students in Grades 8-10.

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