Math Problem Statement

Without calculating, how do you know that the equation |4x - 7| = -1 has no solution?

Solution

The equation 4x7=1|4x - 7| = -1 has no solution because the absolute value, 4x7|4x - 7|, is always non-negative (i.e., zero or positive) for any real number xx. It cannot equal a negative number. Therefore, there are no values of xx that can satisfy the equation where the absolute value equals -1.

Would you like to explore more about absolute value equations or have any other questions?

  1. What is the definition of absolute value?
  2. How would you solve 4x7=5|4x - 7| = 5?
  3. Can an absolute value equation have more than two solutions?
  4. Why can the absolute value function never yield a negative result?
  5. How can graphing 4x7|4x - 7| help understand solutions to equations involving absolute values?

Tip: Always remember that absolute values are defined to measure the "distance" of a number from zero on the number line, which means they can only yield zero or positive values.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value Equations

Formulas

|x| ≥ 0 for all x

Theorems

Properties of Absolute Value

Suitable Grade Level

Grades 7-10