Math Problem Statement

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

Solution

We are given the absolute value equation:

2x5+10=5|2x - 5| + 10 = 5

Step 1: Isolate the absolute value expression

Subtract 10 from both sides:

2x5=510|2x - 5| = 5 - 10 2x5=5|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 2x5=5|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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value Equations

Formulas

|ax + b| = c
Basic algebraic isolation techniques

Theorems

Properties of absolute value
No solution when absolute value equals a negative number

Suitable Grade Level

Grades 8-10