Solve for all values of a,a in simplest form.
4, equals, open vertical bar, minus, 3, a, plus, 4, close vertical bar


The given equation is:

\[
4 = | -3a + 4 |
\]

### Step 1: Understand the absolute value equation

The absolute value equation \( | -3a + 4 | = 4 \) implies that there are two possible cases for \( -3a + 4 \), because the absolute value of an expression is its distance from 0 and is always non-negative.

### Step 2: Set up the two cases

1. \( -3a + 4 = 4 \)
2. \( -3a + 4 = -4 \)

### Step 3: Solve each case separately

#### Case 1: \( -3a + 4 = 4 \)
\[
-3a + 4 = 4
\]
Subtract 4 from both sides:
\[
-3a = 0
\]
Divide both sides by -3:
\[
a = 0
\]

#### Case 2: \( -3a + 4 = -4 \)
\[
-3a + 4 = -4
\]
Subtract 4 from both sides:
\[
-3a = -8
\]
Divide both sides by -3:
\[
a = \frac{8}{3}
\]

### Step 4: Final Solution

The solutions are:

\[
a = 0 \quad \text{or} \quad a = \frac{8}{3}
\]

Would you like further details or have any questions? Here are 5 related questions you might find interesting:

1. How do you solve absolute value equations in general?
2. What are the properties of absolute value functions?
3. What are the graphical interpretations of absolute value equations?
4. Can an absolute value equation have no solutions?
5. What happens when you square both sides of an absolute value equation?

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

Solve for all values of a: 4 = | -3a + 4 |

Learn how to solve the absolute value equation 4 = | -3a + 4 | with a step-by-step solution. This problem involves key algebraic concepts, such as absolute value equations and their properties. Suitable for students in Grades 7-9.

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