https://file.aiquickdraw.com/mathbot/file/1726888962234gg45zkbi.jpg

The equation provided is:

\[
|4b - 5| = 19
\]

This is an absolute value equation. To solve it, we can split it into two cases, based on the definition of absolute value:

### Case 1:
\[
4b - 5 = 19
\]
Solve for \(b\):

\[
4b = 19 + 5 = 24
\]
\[
b = \frac{24}{4} = 6
\]

### Case 2:
\[
4b - 5 = -19
\]
Solve for \(b\):

\[
4b = -19 + 5 = -14
\]
\[
b = \frac{-14}{4} = -3.5
\]

### Final solution:
The values of \(b\) are:
\[
b = 6 \quad \text{or} \quad b = -3.5
\]

Would you like any further clarification on this? Here are some related questions:

1. How do you solve absolute value inequalities?
2. What happens if the absolute value equation has no solution?
3. How does graphing help in understanding absolute value functions?
4. What if the number on the right side of the equation was negative, like \(|4b - 5| = -19\)?
5. How do absolute value transformations affect their graphs?

**Tip:** Always check both cases when solving absolute value equations to ensure all possible solutions are considered.

Learn how to solve the absolute value equation |4b - 5| = 19 with a step-by-step guide. This problem involves key algebraic concepts such as absolute values, leading to two possible solutions. Perfect for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation