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Chapter 11: Problem 4

If \(A=2 x-(y-2 c)\) and \(B=(2 x-y)-2 c,\) then \(A-B=\) a. \(-2 y\) b. \(-4 c\) c. \(-0\) d. \(-2 y\) e. \(-4 c\)

Short Answer

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Step by step solution

01

Substitute the values of A and B into A-B

To start, let’s input the given values of \(A\) and \(B\) into the expression \(A-B\). This gives us \((2x - (y - 2c)) - ((2x - y) - 2c)\)
02

Carry out the subtraction operation

Now, carefully subtract the expressions within the brackets. Recall rules of changing signs when subtracting expressions. This gives us \(2x - y + 2c - 2x + y - 2c\)
03

Simplify the resulting expression

Upon simplifying, we can clearly see that every term cancels each other out (positive 2x cancels negative 2x, negative y cancels positive y, positive 2c cancels negative 2c), leaving us with \(0\)

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Most popular questions from this chapter

If \(a\) is multiplied by 3 and the result is 4 less than 6 times \(b,\) what is the value of \(a-2 b ?\) a. -12 b. \(-\frac{4}{3}\) c. \(-\frac{3}{4}\) d. \(\frac{4}{3}\) e. 12

The original selling price of an item at a store is 40 percent more than the cost of the item to the retailer. If the retailer reduces the price of the item by 15 percent of the original selling price, then the difference between the reduced price and the cost of the item to the retailer is what percent of the cost of the item to the retailer?

$$x^{2}+8 x=-7$$ $$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ x & 0 \end{array}$$ a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal d. The relationship cannot be determined from the information given.

If \(6 k-5 l=27\) and \(3 l-2 k=-13\) and \(5 k-5 l=j,\) what is the value of \(j ?\)

$$11 x+14 y=30 \text { and } 3 x+4 y=12$$ $$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ x+y & (x+y)^{-2} \end{array}$$ a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.
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