Question

Solve for f
Manipulating equations

Answer 1

`\mapsto\large\boxed{f=a-\cfrac{bc}{d}}`

Explanation:

Key Concept

We can manipulate any equation for the variable we want, if we use basic algebra.

`\dotfill`

Our equation is:

`\implies\quad\sf{a=\cfrac{bc}{d}+f}`

Subtract the fraction from both sides:

`\implies\quad\sf{a-\cfrac{bc}{d}=f}`

We're done ! We have now solved for f.

Answer 2

`f=a-(bc)/(d)`

Explanation:

To solve the literal equation for the variable 'f,' you need to isolate 'f' on one side of the equation. Follow these steps:

Step 1: Start with the given equation:

`\Longrightarrow a = (bc)/(d)+f`

Step 2: Subtract 'bc/d' from both sides of the equation to isolate 'f':

`\Longrightarrow a-(bc)/(d) = (bc)/(d)-(bc)/(d)+f\\\\\\\\\therefore \boxed{\boxed{f=a-(bc)/(d) }}`

Now, 'f' is isolated on the right side of the equation.

`\hrulefill`

Additional Information:

Literal Equation: A literal equation is a type of equation that involves two or more variables, where the goal is to solve for one of the variables in terms of the others. In other words, a literal equation expresses a relationship between the variables using mathematical operations such as addition, subtraction, multiplication, and division. Unlike standard algebraic equations that usually have just one variable, literal equations contain multiple variables and are commonly used to represent real-world situations that involve various quantities.