Andy and Sylvie each incorrectly simplified the expression -3 - 4(2x - 3). Andy wrote -14x + 21 and Sylvie wrote -8 - 6. Explain their errors and give the correct answer.
My answer: What Andy did wrong is adding instead of subtracting and adding the negative in the wrong place. What Sylvie did wrong is that there is no variable included in her expression and she subtracted wrong. The correct answer is supposed to be -14x - (-21) or -15 - 8x.
Am I wrong?
The figures show the dimensions of a tennis court and a basketball court given in terms of the width x in feet of the tennis court.
Tennis: W:x L: 2x + 6
Basketball: W:1/2x + 32 L: 3x - 14
A: Write an expression for the perimeter of each court.
B: Write an expression that describes how much greater the perimeter of the basketball court is than the perimeter of the tennis court.
C: Suppose the tennis court is 36 feet wide. Find all dimensions of the two courts.
My answers:
A: (6x + 12) + (6 1/2x - 46)
B: (6 1/2x - 46) - (6x + 12)
C: (4x + 84) + (6 1/2x - 46)
Am I wrong?
thinks for the answer
Yes, Andy and Sylvie both made errors in their simplification of the expression -3 - 4(2x - 3).
Andy's error:
Andy incorrectly added instead of subtracting the terms. He wrote -14x + 21, which means he added the negative sign in the wrong place. The correct step would be to distribute -4 to the terms inside the parentheses and then combine like terms. Distributing -4 to 2x and -3 gives -8x + 12. Then, we have -3 - 8x + 12. Combining like terms, we get -8x + 9. Therefore, Andy's mistake was adding instead of subtracting, resulting in the incorrect expression -14x + 21.
Sylvie's error:
Sylvie incorrectly simplified the expression without including the variable x. Instead of subtracting the terms inside the parentheses, she subtracted the numbers -8 and 6, resulting in -2. However, this answer does not include the variable x or the simplified expression. To correctly simplify the expression, we need to distribute -4 to the terms inside the parentheses and then combine like terms. Distributing -4 to 2x and -3 gives -8x + 12. Then, we have -3 - 8x + 12. Combining like terms, we get -8x + 9. Therefore, Sylvie's mistake was not including the variable x and subtracting the numbers incorrectly, resulting in the incorrect expression -8 - 6.
The correct answer:
To correctly simplify the expression -3 - 4(2x - 3), we distribute -4 to the terms inside the parentheses, which gives us -8x + 12. Then, we have -3 - 8x + 12. Finally, we combine like terms to get the simplified expression -8x + 9. Hence, the correct answer is -8x + 9.
On the first one,
-3 - 4(2x - 3)
-3 - 8x + 12
-8x+9
Andy did (-4-3)(2x-3)
For the next one,
(A) perimeters
Tennis: 2(W+L) = 2(x + 2x+6) = 6x+12
Basketball: 2(W+L) = 2(x/2+32 + 3x-14) = 7x+36
(B) (7x+36)-(6x+12) = x+24
(C) x/2 + 32 = 36
x/2 = 4
x = 8
Tennis: 8x22
Basketball: 36x10