ISEE Word Problems Question 186: Answer and Explanation
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Question: 186
7. If |x – 2| = x, then what is the value of x?
- A. –2
- B. –1
- C. 0
- D. 1
Correct Answer: D
Explanation:
The answer is D
The value inside the absolute value may be negative, zero, or positive, but x itself must be zero or positive because it is equal to the absolute value of a quantity. Thus, it may be that x - 2 = x. Subtract x from both sides: -2 = -2x. Divide both sides by -2: 1 = x. This is an answer, so you may stop here. However, it may also be that -(x - 2) = x. Distribute the negative sign: -x + 2 = x. Add x to both sides: 2 = 2x. Divide both sides by 2: 1 = x.
Test the answers to determine which one makes the equation true.