Question
Solve the equation and check the result. \( -7=\frac{13 r+68}{7} \) SUBMIT ANSWER
Ask by Nunez Deleon. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( r = -9 \)
Solution
**Step 1: Multiply both sides of the equation by 7**
Given the equation
\[
-7 = \frac{13r + 68}{7}
\]
Multiply each side by 7 to eliminate the denominator:
\[
-7 \times 7 = 13r + 68 \quad \Rightarrow \quad -49 = 13r + 68
\]
**Step 2: Isolate \( r \)**
Subtract 68 from both sides to isolate the term containing \( r \):
\[
-49 - 68 = 13r \quad \Rightarrow \quad -117 = 13r
\]
Divide both sides by 13:
\[
r = \frac{-117}{13} = -9
\]
**Step 3: Check the solution**
Substitute \( r = -9 \) back into the original equation:
\[
\frac{13(-9) + 68}{7} = \frac{-117 + 68}{7} = \frac{-49}{7} = -7
\]
Since the left-hand side equals the right-hand side, the solution is correct.
**Final Answer:**
\[
r = -9
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To solve the equation, first multiply both sides by 7 to eliminate the fraction: \[ -7 \times 7 = 13r + 68 \] This simplifies to: \[ -49 = 13r + 68 \] Next, isolate \(13r\) by subtracting 68 from both sides: \[ -49 - 68 = 13r \] This results in: \[ -117 = 13r \] Now, divide both sides by 13: \[ r = \frac{-117}{13} = -9 \] To check the result, substitute \(r = -9\) back into the original equation: \[ -7 = \frac{13(-9) + 68}{7} \] This becomes: \[ -7 = \frac{-117 + 68}{7} \] Which simplifies to: \[ -7 = \frac{-49}{7} = -7 \] Since both sides of the equation are equal, the solution \(r = -9\) is correct.
