Math Problem Statement

x βˆ’ 1 | |

11 | 3 | π‘₯ βˆ’ 1 | |

1 1

Solution

It looks like you're trying to solve the absolute value equation:

∣xβˆ’1∣=11|x - 1| = 11

Step 1: Remove Absolute Value by Setting Two Cases

The definition of absolute value states that if ∣A∣=B|A| = B, then:

A=BorA=βˆ’BA = B \quad \text{or} \quad A = -B

So, applying this to our equation:

  1. xβˆ’1=11x - 1 = 11
  2. xβˆ’1=βˆ’11x - 1 = -11

Step 2: Solve for xx

Case 1: xβˆ’1=11x - 1 = 11

x=11+1=12x = 11 + 1 = 12

Case 2: xβˆ’1=βˆ’11x - 1 = -11

x=βˆ’11+1=βˆ’10x = -11 + 1 = -10

Final Answer:

x=12,βˆ’10x = 12, -10

Would you like me to explain anything further? Here are five related questions:

  1. How do you solve absolute value inequalities?
  2. What happens if an absolute value equation has no solution?
  3. Can absolute value equations have more than two solutions?
  4. How do you graph absolute value functions?
  5. What are some real-world applications of absolute value equations?

Tip: When solving absolute value equations, always check for extraneous solutions in more complex cases.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value Equations

Formulas

|A| = B β†’ A = B or A = -B

Theorems

Definition of Absolute Value

Suitable Grade Level

Grades 7-9