Question

1. which of the following expressions is equivalent to $\frac{12x + 20}{2}$?
2. $24x+10$
3. $2(12x + 20)$
4. $\frac{1}{2}(12x + 20)$
5. $12x + 40$
6. what is the solution to the equation below? $4-3(2x + 1)=7$
7. which of the following is not a helpful first - step in solving the equation below? $\frac{1}{6}(2x + 5)=10$
8. distribute the $\frac{1}{6}$ to the $2x$ and $5$
9. multiply both sides by $\frac{1}{6}$
10. subtract 5 from both sides
11. divide both sides by $\frac{1}{6}$
12. esther is getting a new cell phone. she must pay for the phone itself and then pay a monthly fee for her calls and data. if her total costs for $m$ months are given by the expression $32.50m + 99$, what does the value $32.50$ represent?
13. the cost per month
14. the total cost for one year
15. the cost of the phone
16. the average cost of cell phone plans

Explanation:

Step1: Analyze the equation \(-\frac{1}{6}(2x + 5)=10\)

To solve for \(x\), we first want to get rid of the coefficient \(-\frac{1}{6}\) attached to the parenthesis. The natural first - step is to multiply both sides by \(- 6\) (the reciprocal of \(-\frac{1}{6}\)) to isolate the expression inside the parenthesis. Distributing \(-\frac{1}{6}\) first would make the equation more complex initially.

Step2: Check each option

1. Distributing \(-\frac{1}{6}\) to \(2x\) and \(5\) gives \(-\frac{1}{6}\times2x-\frac{1}{6}\times5=-\frac{1}{3}x-\frac{5}{6}=10\). This is a more complex form and not a helpful first - step.
2. Multiplying both sides by \(-6\) would be a correct first - step as it simplifies the equation to \(2x + 5=-60\).
3. Subtracting \(5\) from both sides is a step that comes after we have dealt with the coefficient \(-\frac{1}{6}\) in front of the parenthesis.
4. Dividing both sides by \(-\frac{1}{6}\) is equivalent to multiplying by \(-6\) and is a correct first - step.

So the answer to the question "Which of the following is not a helpful first step in solving the equation \(-\frac{1}{6}(2x + 5)=10\)" is: 1. Distribute the \(-\frac{1}{6}\) to the \(2x\) and \(5\)

Answer:

1. Distribute the \(-\frac{1}{6}\) to the \(2x\) and \(5\)