Math Problem Statement
Without calculating, how do you know that the equation |4x - 7| = -1 has no solution?
Solution
The equation has no solution because the absolute value, , is always non-negative (i.e., zero or positive) for any real number . It cannot equal a negative number. Therefore, there are no values of 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?
- What is the definition of absolute value?
- How would you solve ?
- Can an absolute value equation have more than two solutions?
- Why can the absolute value function never yield a negative result?
- How can graphing 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