Question
Use algebra to solve for \( x \) in the equation \( 3 x+8=9 x-7 \). If your answer is a fraction, write it in reduced, fractional form. Do NOT convert the answer to a decimal. \( x=\square \)
Ask by Peters Watson. in the United States
Jan 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = \frac{5}{2} \)
Solution
To solve the equation \( 3x + 8 = 9x - 7 \) for \( x \), follow these steps:
1. **Subtract \( 3x \) from both sides** to get all the \( x \)-terms on one side:
\[
3x + 8 - 3x = 9x - 7 - 3x \\
8 = 6x - 7
\]
2. **Add 7 to both sides** to isolate the term with \( x \):
\[
8 + 7 = 6x - 7 + 7 \\
15 = 6x
\]
3. **Divide both sides by 6** to solve for \( x \):
\[
\frac{15}{6} = x
\]
4. **Simplify the fraction**:
\[
x = \frac{5}{2}
\]
**Answer:**
\[
x = \frac{5}{2}
\]
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Simplify this solution Bonus Knowledge
To solve for \( x \) in the equation \( 3x + 8 = 9x - 7 \), start by isolating the variable on one side. First, subtract \( 3x \) from both sides: \[ 8 = 9x - 3x - 7 \] This simplifies to: \[ 8 = 6x - 7 \] Next, add \( 7 \) to both sides: \[ 8 + 7 = 6x \] This gives you: \[ 15 = 6x \] Now, divide both sides by \( 6 \): \[ x = \frac{15}{6} \] To reduce the fraction, divide the numerator and denominator by \( 3 \): \[ x = \frac{5}{2} \] So, the final answer is \( x = \frac{5}{2} \).
