Question

1. the cost of a membership to costco depends on the number of months. the formula used to calculate the total cost is y = 35x, where y is the total cost and x is the number of months. what is the meaning of the 35 in the equation? (a) 35 months per dollar (b) 35 months per dollar (c) 35 dollars per month (d) 35 dollars a year 4. solve for x: 3(x - 6) = -2(x + 1) - 4 (a) x = 16/5 (b) x = 24/5 (c) x = 5/12 (d) x = 12 5. which equation below has only one solution? (a) x - 1 = (4x - 4)/4 (b) 2x - 5 = 5 + 2x (c) 3x - 1 = -3 + 3x (d) 2x - 1 = -1x + 2 6. simplify the expression below. 4x + 1 - (-5x - 3) (a) -x + 4 (b) -x - 2 (c) 9x + 4 (d) 9x - 2

Explanation:

3.

Step1: Analyze the formula $y = 35x$

In the formula $y = 35x$, $y$ is the total cost and $x$ is the number of months. The coefficient 35 represents the cost per - month.

Step1: Expand the equation

Expand $3(x - 6)=-2(x + 1)-4$.
$3x-18=-2x - 2-4$.

Step2: Combine like - terms

$3x+2x=-2 - 4 + 18$.
$5x = 12$.

Step3: Solve for $x$

$x=\frac{12}{5}$.

Step1: Solve equation (a)

$x - 1=\frac{4x-4}{4}$, simplify the right - hand side: $\frac{4x - 4}{4}=x - 1$, which is an identity, has infinitely many solutions.

Step2: Solve equation (b)

$2x-5 = 5 + 2x$, subtract $2x$ from both sides: $-5=5$, which is a contradiction, has no solutions.

Step3: Solve equation (c)

$3x-1=-3 + 3x$, subtract $3x$ from both sides: $-1=-3$, which is a contradiction, has no solutions.

Step4: Solve equation (d)

$2x-1=-x + 2$, add $x$ to both sides: $3x-1 = 2$, then add 1 to both sides: $3x=3$, divide by 3: $x = 1$. It has one solution.

Answer:

(c) 35 dollars per month

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