To solve the equation:

\[
\frac{|x - 4|}{2} + 10 = 7
\]

### Step 1: Isolate the absolute value expression
First, subtract 10 from both sides of the equation to isolate the absolute value term:

\[
\frac{|x - 4|}{2} = 7 - 10
\]
\[
\frac{|x - 4|}{2} = -3
\]

### Step 2: Check for a valid solution
Since the absolute value function, \(|x - 4|\), always gives a non-negative result (greater than or equal to 0), it is impossible for \(\frac{|x - 4|}{2}\) to equal \(-3\). Therefore, there is **no solution** for this equation.

Would you like further details or have any questions?

### Related Questions:
1. How do you solve absolute value equations in general?
2. What happens if the right-hand side of an equation is negative in absolute value equations?
3. Can an absolute value equation have multiple solutions?
4. How do you solve absolute value inequalities?
5. What are the properties of absolute value functions?

### Tip:
When solving absolute value equations, always check if the equation leads to a possible solution since the absolute value cannot produce a negative result.

Learn how to solve the absolute value equation |x - 4|/2 + 10 = 7, step by step. This problem explores key algebra concepts such as isolating absolute value terms and checking for valid solutions. Appropriate 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