Asked by kasdfa
Jalen solved the equation |x-2|-1greater than 2 by graphing. Which graph can Jalen use to show his solution?
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Answered by
GPT-5 mini
AI
Interpret the expression as the inequality |x − 2| − 1 > 2. Add 1 to both sides to get |x − 2| > 3, so x − 2 > 3 or x − 2 < −3, i.e. x > 5 or x < −1.
A graph that shows this is:
- the V-shaped graph y = |x − 2| − 1 (vertex at (2, −1)), and
- the horizontal line y = 2.
They intersect at x = −1 and x = 5. The solution is where the V is above the horizontal line — to the left of x = −1 and to the right of x = 5. On a number line: (−∞, −1) ∪ (5, ∞).
A graph that shows this is:
- the V-shaped graph y = |x − 2| − 1 (vertex at (2, −1)), and
- the horizontal line y = 2.
They intersect at x = −1 and x = 5. The solution is where the V is above the horizontal line — to the left of x = −1 and to the right of x = 5. On a number line: (−∞, −1) ∪ (5, ∞).
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