4. Compare the quantity in Column A with the quantity in Column B.
Column A
The solution of
2(x-3) = 6x
Column B
The solution of
3x + 2 + 5x + 6
Compare the quantity in Column A with the quantity in Column B.
Column A
6z-5 if z=-2
Column B
-6z – 5 if z = 2
Answer-The quantities are equal
Evaluate 2y^2(x+y) when x =8 and y=3
Answer-198
Evaluate 2y^2(x+y) when x =8 and y=3
2(3^2)(8+3)
=2(9)(11)
=198
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Column A
6z-5 if z=-2
6(-2)-5
=-12-5
=-17
Column B
-6z – 5 if z = 2
-6(2)-5
=-17
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Column A
The solution of
2(x-3) = 6x
2x-6 = 6x
4x=-6
x=-3/2
Column B
The solution of (note typo assumed)
3x + 2 = 5x + 6
2x=2-6
x=-4/2=-2
To compare the quantities in Column A and Column B, we need to solve the equations in each column separately and then compare the solutions.
Let's start with Column A:
The equation in Column A is 2(x-3) = 6x.
1. Distribute the 2 to the terms inside the parentheses: 2x - 6 = 6x.
2. Subtract 2x from both sides of the equation: -6 = 4x.
3. Divide both sides of the equation by 4 to solve for x: x = -6/4 = -3/2.
So the solution to the equation in Column A is x = -3/2.
Now let's move to Column B:
The equation in Column B is 3x + 2 + 5x + 6.
1. Combine like terms: 8x + 8.
2. Simplify if possible: 8(x + 1).
So the solution to the equation in Column B is x + 1.
To compare the quantities, we have:
Column A: x = -3/2
Column B: x + 1
Since we don't have an exact value for the solution in Column B, we cannot directly compare the quantities. However, we can substitute the value we found for x in Column A into the expression in Column B to see if the values are equal.
Using the solution from Column A (x = -3/2), we have:
Column B: (-3/2) + 1 = -3/2 + 2/2 = -1/2
So, Column A is -3/2 and Column B is -1/2.
Based on this comparison, we can conclude that the quantity in Column A is greater than the quantity in Column B.