Problem 77 - College Algebra Essentials

Question

Explain what it means to solve a formula for a variable.

Step-by-Step Solution

Answer

Solving a formula for a variable means manipulating the formula in such a way that one specific variable is by itself on one side of the equation. This is often done by applying the inverse operations to isolate the desired variable.

Step 1: Understand the concept of a formula

A formula is a mathematical rule or relationship that uses symbols to represent a quantity. It's a way of expressing information in terms of symbols. For example, the formula for the area of a rectangle is \(A = l \times w\), where \(A\) is the area, \(l\) is the length, and \(w\) is the width.

Step 2: Identify the Variable to Solve For

Decide which variable you're solving for in this formula. Say you're given the formula \(A = l \times w\) and you are asked to solve for \( l \). This means you want to get \( l \) on one side of the equal sign and everything else on the other side.

Step 3: Isolate the Desired Variable

Get the variable you’re solving for on one side of the equation and all other variables on the other side. This involves using inverse operations. For the area of a rectangle formula, to solve for \( l \), you would divide both sides of the equation by \( w \). So, \( l = A/w \).

Step 4: Check Your Work

You should always check your work to ensure accuracy. For instance, If \( A = 12 \) and \( w = 3 \), then according to the formula \( l = 12/3 = 4\). You can also check by substituting \( l \) and \( w \), into the original formula \(A = l \times w\). If the left-hand side equals the right-hand side then your solution is correct.