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Chapter 11: Problem 7

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

Short Answer

Expert verified
The value of \(a - 2b\) is \(-\frac{4}{3}\). So, the correct answer is (b) \(-\frac{4}{3}\).

Step by step solution

01

Translate the Word Problem to an Algebraic Equation

The given statement 'If \(a\) is multiplied by 3 and the result is 4 less than 6 times \(b\)' can be translated into the equation: \(3a = 6b - 4\)
02

Solve the Equation for \(a\)

Firstly, let's isolate \(a\) on one side of the equation. This can be done by dividing everything by 3. Therefore, you get: \(a = 2b - \frac{4}{3}\)
03

Solve for \(a - 2b\)

Now we want to find the value of \(a - 2b\). We substitute the expression \(a = 2b - \frac{4}{3}\) into \(a - 2b\). This will give us: \(a - 2b = (2b - \frac{4}{3}) - 2b\). When we simplify this, we end up with \(-\frac{4}{3}\).

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Most popular questions from this chapter

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?

$$11 x+14 y=30 \text { and } 3 x+4 y=12$$ Quantity \(\mathbf{A}\) \(x+y\) Quantity \(\mathbf{B}\) \\[ (x+y)^{-2} \\] 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.

Quantity \(\mathbf{A}\) $$\frac{2^{-4}}{4^{-2}}$$ Quantity_B $$\frac{\sqrt{64}}{-2^{3}}$$ 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.

A merchant sells three different sizes of canned tomatoes. A large can costs the same as 5 medium cans or 7 small cans. If a customer purchases an equal number of small and large cans of tomatoes for the same amount of money needed to buy 200 medium cans, how many small cans does she purchase? a. 35 b. 45 c. 72 d. 99 e. 208

$$x^{2}+8 x=-7$$ Quantity \(\mathbf{A}\) \(x\) Quantity_B 0 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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