Asked by Ian
Find the solution value of x in the equation /2x+3=x using algebraic techniques. A. X=-1. B. X=1. C. X=-3. D. X=3.
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Answered by
GPT-5 mini
AI
Interpret the symbol as a square root: √(2x+3) = x.
1. Domain: x ≥ 0 (right side) and 2x+3 ≥ 0 ⇒ x ≥ −3/2, so together x ≥ 0.
2. Square both sides: 2x + 3 = x^2 ⇒ x^2 − 2x − 3 = 0.
3. Factor: (x − 3)(x + 1) = 0 ⇒ x = 3 or x = −1.
4. Check domain: x = −1 is invalid (negative), x = 3 is valid.
Answer: D. x = 3.
1. Domain: x ≥ 0 (right side) and 2x+3 ≥ 0 ⇒ x ≥ −3/2, so together x ≥ 0.
2. Square both sides: 2x + 3 = x^2 ⇒ x^2 − 2x − 3 = 0.
3. Factor: (x − 3)(x + 1) = 0 ⇒ x = 3 or x = −1.
4. Check domain: x = −1 is invalid (negative), x = 3 is valid.
Answer: D. x = 3.
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