solve the absolute value equation /2x-5/+10=5

We are given the absolute value equation:

\[
|2x - 5| + 10 = 5
\]

### Step 1: Isolate the absolute value expression

Subtract 10 from both sides:

\[
|2x - 5| = 5 - 10
\]
\[
|2x - 5| = -5
\]

### Step 2: Analyze the equation

Since the absolute value of any expression is always non-negative (i.e., it must be greater than or equal to 0), there is no solution when the absolute value equals a negative number.

Thus, there is **no solution** to the equation.

Would you like more details, or do you have any questions?

### Related Questions:
1. How do you solve absolute value inequalities?
2. Can absolute value equations have no solution?
3. What if the equation were \( |2x - 5| = 5 \)?
4. How do absolute value functions affect graphing?
5. What are the steps for solving more complex absolute value equations?

### Tip:
Always check if isolating the absolute value leads to a negative number—if it does, the equation has no solution.

Learn how to solve the absolute value equation |2x - 5| + 10 = 5 with a detailed, step-by-step solution. Discover why there is no solution due to the properties of absolute value. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation