make f the subject of the formular: f+a = 2f+3 over a

To make \( f \) the subject of the formula \( \frac{f + a}{a} = 2f + 3 \), follow these steps:

### Step 1: Eliminate the denominator
Multiply both sides by \( a \) to remove the fraction:
\[
f + a = a(2f + 3)
\]

### Step 2: Distribute the \( a \) on the right-hand side
\[
f + a = 2af + 3a
\]

### Step 3: Move all terms involving \( f \) to one side of the equation
Subtract \( f \) from both sides:
\[
a = 2af + 3a - f
\]

### Step 4: Factor \( f \) on the right-hand side
\[
a = f(2a - 1) + 3a
\]

### Step 5: Isolate \( f \)
Subtract \( 3a \) from both sides:
\[
a - 3a = f(2a - 1)
\]
\[
-2a = f(2a - 1)
\]

### Step 6: Solve for \( f \)
Divide both sides by \( 2a - 1 \):
\[
f = \frac{-2a}{2a - 1}
\]

So, the formula with \( f \) as the subject is:
\[
f = \frac{-2a}{2a - 1}
\]

Would you like more details on any of these steps or have further questions?

Here are some related questions for practice:

1. How would you isolate \( f \) if the original formula was \( \frac{f + 2a}{a} = 2f + 3 \)?
2. How do you handle the equation if there’s a different constant multiplied by \( f \) on the right-hand side?
3. What happens if \( a = 0 \) in the final solution?
4. Can you derive a similar formula where the roles of \( f \) and \( a \) are swapped?
5. How do you simplify a formula like this if you need to substitute specific values for \( a \)?

**Tip:** Always check for potential divisions by zero when solving equations with variables in the denominator.

make f the subject of the formula: (f + a)/a = 2f + 3

Learn how to make f the subject of the formula (f + a)/a = 2f + 3 with a step-by-step solution. This problem involves algebraic concepts like isolating a variable, applying the distributive property, and solving linear equations. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation