Question
Austin worked out the problem to the left and got an answer of "x" equals 7.
Lisa thinks he made a mistake and the answer should be "x" equals 1.
Who is correct or are they both wrong? Why?
Explain your thinking.
Lisa thinks he made a mistake and the answer should be "x" equals 1.
Who is correct or are they both wrong? Why?
Explain your thinking.
Answers
Answered by
GPT-5 mini
I don’t see the actual problem — could you paste the equation or upload the image? Without it I can’t tell which answer is right.
How you (or I) can check quickly once you share the problem:
1. Substitute x = 7 and x = 1 into the original equation/expression. Whichever value makes the original true is a correct solution.
2. Check the domain: if the original contains a square root, logarithm, or a denominator that could be zero, one of the answers might be invalid even if it satisfies an algebraic step.
3. Be careful about steps that produce extraneous solutions (squaring both sides, multiplying by an expression that could be zero, taking absolute values, etc.). If you used such a step, verify candidates in the original.
Examples:
- If the original equation was x^2 − 8x + 7 = 0, then both 1 and 7 are correct (it factors to (x−1)(x−7)=0).
- If the original was 2^x = 128, then x = 7 is correct (2^7 = 128) and x = 1 is wrong.
- If the original was √(x+3) = x − 1, then neither 1 nor 7 is the solution (you must solve and check domain).
Send the exact problem and I’ll tell you which of Austin or Lisa is right and why.
How you (or I) can check quickly once you share the problem:
1. Substitute x = 7 and x = 1 into the original equation/expression. Whichever value makes the original true is a correct solution.
2. Check the domain: if the original contains a square root, logarithm, or a denominator that could be zero, one of the answers might be invalid even if it satisfies an algebraic step.
3. Be careful about steps that produce extraneous solutions (squaring both sides, multiplying by an expression that could be zero, taking absolute values, etc.). If you used such a step, verify candidates in the original.
Examples:
- If the original equation was x^2 − 8x + 7 = 0, then both 1 and 7 are correct (it factors to (x−1)(x−7)=0).
- If the original was 2^x = 128, then x = 7 is correct (2^7 = 128) and x = 1 is wrong.
- If the original was √(x+3) = x − 1, then neither 1 nor 7 is the solution (you must solve and check domain).
Send the exact problem and I’ll tell you which of Austin or Lisa is right and why.