Question

5. Geraldo was solving the radical equation √√-3x +21= x - 7. His work is shown below. Explain what

mistake Geraldo made in his work. You DO NOT have to show the correct work, just explain his mistake.
-2
√√-3x +21² = (x-7) ²
२
-3x+21= X-7
-X
-X
-4x + 21 = -7
-21 -21
-4x = -28
-4 -4
X=7

Answer 1

Geraldo’s mistake occurred in steps 3 and 6, where he incorrectly subtracted and divided by positive x instead of negative x.

Explanation:

Geraldo made a mistake in his work while solving the radical equation √√-3x +21= x - 7. The mistake occurred when he squared both sides of the equation. Let’s go through his work step by step to identify the error:

1.Geraldo squared both sides of the equation: √√-3x +21² = (x-7) ². This step is correct.

2.Geraldo simplified the left side of the equation: -3x+21= X-7. This step is also correct.

3.Geraldo subtracted x from both sides of the equation: -3x+21= X-7. However, he made a mistake in the signs. The correct subtraction should be -X, not X.

4.Geraldo simplified the equation further: -4x + 21 = -7. This step is correct.

5.Geraldo subtracted 21 from both sides of the equation: -4x = -28. This step is also correct.

6. Finally, Geraldo divided both sides of the equation by -4 to solve for x: X=7. However, he made a mistake in the signs again. The correct division should be x = -7.

Therefore, Geraldo’s mistake occurred in steps 3 and 6, where he incorrectly subtracted and divided by positive x instead of negative x.