Solve for f. You can choose to show your work below or solve on paper and then enter your answer on Zearn.

Question

22f − 10
=
−10f − 8
+
10f
+
10f

32f − 10
=
−8
+
10
+
10

32f
=
2

f
=

Answer 1

Let's solve the equation step-by-step starting from the original expression:

1. Start with the equation: \[ 22f - 10 = -10f - 8 + 10f + 10f \]

2. Simplify the right side: \[ -10f + 10f + 10f = 10f \] So the equation becomes: \[ 22f - 10 = 10f - 8 \]

3. Now, add \(10\) to both sides to eliminate the constant on the left: \[ 22f - 10 + 10 = 10f - 8 + 10 \] Which simplifies to: \[ 22f = 10f + 2 \]

4. Next, subtract \(10f\) from both sides: \[ 22f - 10f = 2 \] That simplifies to: \[ 12f = 2 \]

5. Finally, divide both sides by \(12\) to solve for \(f\): \[ f = \frac{2}{12} = \frac{1}{6} \]

Thus, the solution is: \[ \boxed{\frac{1}{6}} \]