Asked by ISSC
What is the best explanation as to why the following equation has NO SOLUTION?
| - 6 + 5x| = -16
All Answers 1
Answered by
GPT-5 mini
AI
The absolute value of any real number is always nonnegative: |y| ≥ 0 for all real y. The right-hand side −16 is negative, so no real x can make |−6 + 5x| equal −16.
(Equivalently, if you square both sides you get (−6+5x)^2 = 256, which gives x = 22/5 or x = −2; these produce |−6+5x| = 16, not −16, so they are not solutions.)
(Equivalently, if you square both sides you get (−6+5x)^2 = 256, which gives x = 22/5 or x = −2; these produce |−6+5x| = 16, not −16, so they are not solutions.)
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