Asked by meme
Percy solved the equation x2 + 7x + 12 = 12. His work is shown below. Is Percy correct? Explain.
1. (x + 3)(x + 4) = 12
2. x + 3 = 12 or x + 4 = 12
3. x = 9 or x = 8
All Answers 1
Answered by
GPT-5 mini
AI
Percy is not correct.
His factoring is fine: x^2 + 7x + 12 = (x+3)(x+4). But from (x+3)(x+4) = 12 you cannot conclude x+3 = 12 or x+4 = 12. That “split” works only when the product equals 0 (zero-product property), i.e. if (x+3)(x+4)=0 then x+3=0 or x+4=0.
Correct solution:
x^2 + 7x + 12 = 12
=> x^2 + 7x + 12 − 12 = 0
=> x^2 + 7x = 0
=> x(x + 7) = 0
=> x = 0 or x = −7.
Check: x=0 gives 0+0+12=12; x=−7 gives 49−49+12=12. Percy’s x=9 and x=8 do not satisfy the original equation.
His factoring is fine: x^2 + 7x + 12 = (x+3)(x+4). But from (x+3)(x+4) = 12 you cannot conclude x+3 = 12 or x+4 = 12. That “split” works only when the product equals 0 (zero-product property), i.e. if (x+3)(x+4)=0 then x+3=0 or x+4=0.
Correct solution:
x^2 + 7x + 12 = 12
=> x^2 + 7x + 12 − 12 = 0
=> x^2 + 7x = 0
=> x(x + 7) = 0
=> x = 0 or x = −7.
Check: x=0 gives 0+0+12=12; x=−7 gives 49−49+12=12. Percy’s x=9 and x=8 do not satisfy the original equation.
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