# Algebra 1/Unit 3: Linear and Literal Equations, and how to solve them

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Here, we will discuss Linear and Literal equations and how to solve them. This lesson might be a bit tricky, but once you master the lesson it will get way more manageable. Let's head onto the lesson.

## Literal Equations

Let's start with the easier one, literal equations. Literal equations typically have a hefty amount of variables. Many of the literal equations you have worked with have been formulas. Although these equations will look different than our normal equations, they still follow the normal rules of solving.

### Examples for "solving" Literal Equations

An example of a literal equation is ${\displaystyle {\text{A = b · h}}}$, this is the formula for finding the area of a rectangle. We are going to simply "solve" for the variable ${\displaystyle {\text{h}}}$ from the equation, we solve this by using the order of operations in reverse and adding, subtracting, multiplying, or diving values to both sides of the equation, to make effectively nothing different.

${\displaystyle {\text{A = b · h}}}$

• When “solving” Literal Equations, we follow the same rules as simple equations. Therefore, in order to solve for ${\displaystyle {\text{h}}}$ in this equation, we need to isolate it by itself. Therefore, we will divide both sides by ${\displaystyle {\text{b}}}$

${\displaystyle {\frac {A}{b}}={\frac {b\cdot h}{b}}}$

• Doing so, the process will isolate ${\displaystyle {\text{h}}}$, giving us the answer:

${\displaystyle {\text{h = }}{\frac {A}{b}}}$

Another example of a literal equation is ${\displaystyle {\text{x = m + n}}}$. We will simply do the same in the last example, isolating ${\displaystyle {\text{m}}}$.

${\displaystyle {\text{x = m + n}}}$

• Using the last example as a reference, in order to solve for and or isolate ${\displaystyle {\text{m}}}$, we will subtract both sides by ${\displaystyle {\text{n}}}$.

${\displaystyle {\text{x}}{\mathit {-n}}{\text{ = m + n}}{\mathit {-n}}}$

• ${\displaystyle {\text{m}}}$ is now isolated.

${\displaystyle {\text{x − n = m}}}$

${\displaystyle {\text{m = x − n}}}$

• Even if there were no numbers, we have "solved" the literal equation for ${\displaystyle {\text{m}}}$