Question
Solve the following equation for \( x \). \[ a x-8=19 \] A \( x=27 a \) B \( \quad x=\frac{a}{27} \) C \( x=\frac{27}{a} \) D \( x=\frac{11}{a} \)
Ask by Edwards Evans. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The answer is \( x = \frac{27}{a} \), choice C.
Solution
To solve the equation \( a x - 8 = 19 \) for \( x \), follow these steps:
1. **Isolate the term with \( x \):**
\[
a x - 8 = 19 \implies a x = 19 + 8 \implies a x = 27
\]
2. **Solve for \( x \) by dividing both sides by \( a \):**
\[
x = \frac{27}{a}
\]
So, the correct solution is:
**C. \( x = \frac{27}{a} \)**
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Bonus Knowledge
To solve the equation \( a x - 8 = 19 \), we first add 8 to both sides: \[ a x = 19 + 8 \] \[ a x = 27 \] Next, we divide both sides by \( a \) (assuming \( a \neq 0 \)): \[ x = \frac{27}{a} \] So the solution is \( x = \frac{27}{a} \), which corresponds to option C.