Question
Solve for \( f \) \[ 8+5 f=-4 f+1+8 f \] \( f=\square \) Submit
Ask by Campbell Fleming. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f = -7 \)
Solution
To solve for \( f \) in the equation:
\[
8 + 5f = -4f + 1 + 8f
\]
**Step 1: Simplify the Right-Hand Side (RHS)**
Combine like terms on the RHS:
\[
-4f + 8f = 4f
\]
So the equation becomes:
\[
8 + 5f = 4f + 1
\]
**Step 2: Isolate the Variable \( f \)**
Subtract \( 4f \) from both sides to get all \( f \)-terms on one side:
\[
8 + 5f - 4f = 1
\]
\[
8 + f = 1
\]
**Step 3: Solve for \( f \)**
Subtract 8 from both sides:
\[
f = 1 - 8
\]
\[
f = -7
\]
**Final Answer:**
\[
f = -7
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve the equation \( 8 + 5f = -4f + 1 + 8f \), we begin by simplifying the right side. Combine like terms on the right: \[ -4f + 8f = 4f \] Now the equation becomes: \[ 8 + 5f = 1 + 4f \] Next, we isolate \( f \) by getting all the terms involving \( f \) on one side and the constants on the other. Subtract \( 4f \) from both sides: \[ 8 + 5f - 4f = 1 \] This simplifies to: \[ 8 + f = 1 \] Now, we isolate \( f \) by subtracting 8 from both sides: \[ f = 1 - 8 \] \[ f = -7 \] Thus, the solution is: \( f = -7 \)
