Solve for all values of bb in simplest form.
open vertical bar, 4, b, plus, 10, close vertical bar, equals, 12
∣4b+10∣=
12

We are given the equation:

\[
|4b + 10| = 12
\]

### Step 1: Understanding Absolute Value
The absolute value equation \( |x| = a \) means that \( x = a \) or \( x = -a \), provided \( a \geq 0 \).

### Step 2: Break the Equation into Two Cases

#### Case 1: \( 4b + 10 = 12 \)
Solve for \( b \):

\[
4b + 10 = 12
\]
Subtract 10 from both sides:
\[
4b = 2
\]
Divide both sides by 4:
\[
b = \frac{2}{4} = \frac{1}{2}
\]

#### Case 2: \( 4b + 10 = -12 \)
Solve for \( b \):

\[
4b + 10 = -12
\]
Subtract 10 from both sides:
\[
4b = -22
\]
Divide both sides by 4:
\[
b = \frac{-22}{4} = \frac{-11}{2}
\]

### Step 3: Final Answer
The solutions for \( b \) are:

\[
b = \frac{1}{2} \quad \text{or} \quad b = \frac{-11}{2}
\]

Would you like more details on any of these steps?

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Here are 5 related questions:
1. How do we solve absolute value inequalities?
2. What happens if the absolute value equals a negative number?
3. How do you solve absolute value equations with variables on both sides?
4. How can we visualize absolute value functions on a graph?
5. What are the properties of absolute values in terms of distance?

**Tip:** When solving absolute value equations, always consider both the positive and negative scenarios.

Solve for all values of b in simplest form. |4b + 10| = 12

Learn how to solve the absolute value equation |4b + 10| = 12 with a detailed step-by-step solution. This solution breaks the problem into two cases, covers key algebraic concepts, and applies the absolute value property. Suitable for students in Grades 7-9.

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