https://file.aiquickdraw.com/mathbot/file/1729007876569nsodxpfd.jpg

The given equation is:

\[
21 = |5 - 4b|
\]

This is an absolute value equation, so to solve it, we need to consider two cases:

### Case 1: \( 5 - 4b = 21 \)
In this case, we simply remove the absolute value and solve the linear equation:
\[
5 - 4b = 21
\]
Subtract 5 from both sides:
\[
-4b = 21 - 5
\]
\[
-4b = 16
\]
Now, divide both sides by -4:
\[
b = \frac{16}{-4}
\]
\[
b = -4
\]

### Case 2: \( 5 - 4b = -21 \)
In this case, the expression inside the absolute value is equal to -21:
\[
5 - 4b = -21
\]
Subtract 5 from both sides:
\[
-4b = -21 - 5
\]
\[
-4b = -26
\]
Now, divide both sides by -4:
\[
b = \frac{-26}{-4}
\]
\[
b = \frac{26}{4}
\]
Simplifying the fraction:
\[
b = \frac{13}{2}
\]

### Solution:
The two possible values of \( b \) are:
\[
b = -4 \quad \text{or} \quad b = \frac{13}{2}
\]

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. How would you solve \( 30 = |7 - 3b| \)?
2. What happens when the absolute value is zero, i.e., \( |x| = 0 \)?
3. Solve \( 18 = |6 - 2b| \) for all values of \( b \).
4. What is the general approach for solving absolute value inequalities?
5. How do you check if your solutions to absolute value equations are correct?

**Tip:** Always consider both positive and negative cases when solving absolute value equations.

Solve for all values of b in simplest form: 21 = |5 - 4b|

This page explains how to solve the absolute value equation 21 = |5 - 4b| step by step. It covers essential algebraic concepts such as absolute value properties and solving linear equations, suitable for students in Grades 7-9.

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