https://file.aiquickdraw.com/mathbot/file/17267823403116ihqlf94.jpg

The equation from the image is:

\[
-4 + 5|5x + 3| = 21
\]

Let's solve this step by step:

### Step 1: Isolate the absolute value expression
We first isolate the absolute value term \( |5x + 3| \):

\[
5|5x + 3| = 21 + 4
\]

\[
5|5x + 3| = 25
\]

### Step 2: Solve for the absolute value
Now, divide both sides by 5:

\[
|5x + 3| = 5
\]

### Step 3: Remove the absolute value
The equation \( |5x + 3| = 5 \) splits into two cases:

#### Case 1: \( 5x + 3 = 5 \)
\[
5x = 5 - 3
\]
\[
5x = 2
\]
\[
x = \frac{2}{5}
\]

#### Case 2: \( 5x + 3 = -5 \)
\[
5x = -5 - 3
\]
\[
5x = -8
\]
\[
x = \frac{-8}{5}
\]

### Step 4: Final solutions
Thus, the two solutions are:
\[
x = \frac{2}{5} \quad \text{or} \quad x = \frac{-8}{5}
\]

Would you like further explanation on any step?

Here are some related questions:
1. How do you handle absolute value equations?
2. What are the different cases in absolute value equations?
3. How would this problem change if the equation were an inequality?
4. How can you check the solutions by substituting them back into the original equation?
5. What are some real-world applications of absolute value equations?

**Tip:** Always isolate the absolute value first when solving equations involving absolute values!

Step-by-step solution of the absolute value equation -4 + 5|5x + 3| = 21. Learn how to handle absolute value equations by isolating and solving for different cases. Suitable for students in Grades 8-10.

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