Let's solve the equation \( 13(6x - 9) = -33 \) step by step and determine the order of the steps.
Question 1: Order of Steps
To solve the equation, the steps are as follows:
-
Step 1: Distribute the 13.
\[
13 \times 6x - 13 \times 9 = -33 \quad \Rightarrow \quad 78x - 117 = -33
\]
-
Step 2: Add 117 to both sides.
\[
78x - 117 + 117 = -33 + 117 \quad \Rightarrow \quad 78x = 84
\]
-
Step 3: Divide both sides by 78.
\[
x = \frac{84}{78} = \frac{14}{13} \quad \text{(which simplifies to } x = \frac{14}{13} \text{ or approximately 1.08)}
\]
However, it seems the choices you've provided for the value of \( x \) are integers. Therefore, we should verify whether our result aligns with any of the options provided in Question 2.
Question 2: Solve for \(x\)
Let's go through the calculations again to ensure we can relate it to the options provided.
-
Start with:
\[
13(6x - 9) = -33
\]
-
Distribute 13:
\[
78x - 117 = -33
\]
-
Add 117:
\[
78x = -33 + 117 \quad \Rightarrow \quad 78x = 84
\]
-
Divide by 78:
\[
x = \frac{84}{78}
\]
This can be simplified:
\[
x = \frac{14}{13} \quad \text{(approximately 1.08)}
\]
Since we have no matching options from the choices you provided, please verify the given options as none of them matches.
However, if you want to stick to the structured order, the correct sequence of steps is:
- Step 1: Distribute \( 13 \)
- Step 2: Add \( 117 \) to both sides
- Step 3: Divide by \( 78 \)
Given this situation, it's possible that there was a miscommunication or misunderstanding of the correct answer, if this indeed relates to integers; hence you would need to review the context in which this equation was derived. Please check if there is a slight discrepancy in the equation or consider reevaluating the options provided.
1 answer