When trying to solve the equation x2+4x−5=7 , Jamal provide his work in the table above. At what step, if at all, did Jamal make a mistake? What was Jamal's mistake? Explain how the solution is incorrect or correct.

Answer 1

To solve the equation \( x^2 + 4x - 5 = 7 \), we should first simplify it by moving all terms to one side of the equation:

1. Subtract 7 from both sides: \[ x^2 + 4x - 5 - 7 = 0 \] This simplifies to: \[ x^2 + 4x - 12 = 0 \]

Now, we can factor the quadratic equation if possible. The equation \( x^2 + 4x - 12 \) can be factored as follows:

2. We need two numbers that multiply to \(-12\) (the constant term) and add to \(4\) (the coefficient of \(x\)). The numbers are \(6\) and \(-2\): \[ (x + 6)(x - 2) = 0 \]

3. Setting each factor to zero gives: \[ x + 6 = 0 \quad \text{or} \quad x - 2 = 0 \] Therefore: \[ x = -6 \quad \text{or} \quad x = 2 \]

Now, if we look at Jamal's process as described in your question (which isn't provided, but is typically a sequential calculation), we can analyze if he made a mistake:

• If he failed to move all the terms to one side correctly, then he would incorrectly work with the original equation.
• If he calculated \( x^2 + 4x - 5 - 7 \) incorrectly, he may have made an error here, leading to the wrong quadratic to solve.

In conclusion, to identify a mistake:

• Double-check each algebraic manipulation for errors.
• Ensure that he correctly factors the quadratic if that's part of his method.
• The main potential mistake could stem from not simplifying correctly or misinterpreting signs/values during calculation.

Without the specifics of Jamal's work (the table mentioned), it's hard to pinpoint exactly where he went wrong, but common errors often occur during the simplification step or the factoring step.