There is nothing like a straightforward math problem. Literal equations are just that! They are equations where the variables already are known values. Students will learn how to solve for a designated variable in algebraic expressions by properly balancing the equation (though not calculate an actual numerical value for the variable). Below you will find a complete set of introductory material, practice questions, reviews, longer exercise sheets, and quizzes. These worksheets demonstrate how to solve these types of equations by teaching the skill, completing practice worksheets, and reviewing the skill.
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Literal Equations Lesson
This lesson will walk through all the necessary steps to solve literal equation. Learn how to solve equations like the following: Solve for h: B = 1/2 b h.
Solve for the indicated variable in each of these 10 problems. Example: Solve for t: 1/3t = a
Solve for the indicated variable in each of these problems by rearranging and reducing the equations. Example: Solve for a: 1/5a = w 2
Skill Review Sheet
You will be provided with a complete example. Practice this skill by completing the problems below. Example: Solve for u: st - u = v 2
This is a quick assessment to see where you are at with this skill. Solve for the indicated variable in the following problems, then check your answers and score the results. Example: Solve for q: qw + r = t 2
Warm Up or Quick Review
This is a great way to begin a lesson on literal equations. We give students 3 problems and a place to put their inital answer. This is a good way to do a classwide assessment. Here is an example: Solve for k: m - k = h
What are Literal Equations?
Literal equations are your run of the mill equation, but they have at least two variables. They can have more than two variables, but they need to have at least two to qualify as a literal equation. Variables are often referred to as literals. When we approach these problems, at first, we will be a little confused because there are two unknowns in the way. If we rearrange the equation so that one of the literals are expressed relative to the other variable, we can quickly see how to solve problems like this. Your first step should be to choose which variable will be easier to work with. Once you have decided this just rearrange the equation to isolate that variable. You would do the same thing to solve for the remaining variables in the literal equation. This is usually one of the first times that we are introducing students to abstract math. When solving math or physic problems, we often come across specific equations with letters or symbols. Make sure to proceed slowly and take your time with the concepts.
Each of these symbols and letters is referred to as a variable, where each variable represents a value or quantity. The most used variables in such equations are a, b, c, x, y, and z.
When solving literal equations, each variable can be expressed in terms of another, and the goal is to isolate the variable on one side of the equation and the rest on the other.
These variables act just like numbers in a simple equation. They can be added, subtracted, multiplied, and divided (given that the value of the variable that acts as the denominator is not zero) with each other and other numbers.
Some examples of literal equations that you may have come across are:
- The area of the circle: A = ℼr2
- The perimeter of a rectangle: P= 2L + 2W
- Algebraic equations: for example, x + y= 3
- Einstein's mass-energy equation: E = mc2
Some people often confuse simple one-variable equations for literal equations. Literal equations have two or more variables. For example, the equation 2n = n + 1 is not a literal equation as it only contains one variable.
How to Solve Them?
The trick to solving a literal equation is to rearrange the equations so that the variable you want to find/calculate is on one side of the equation, becoming the subject of the equation, while other variables are on the other side.
Once you have rearranged the equation, follow the algebraic rules; adding, subtracting, multiplying, or dividing the variables. Let's look at some examples to help us understand how to solve literal equations.
Example of a One-Step Solution:
Solve for x in the literal equation y = 3x.
In this case, we need to isolate x to one side of the equation and express it in terms of y. To do that, we must remove the coefficient 3 that is multiplying to x. To remove the three, we divide both sides with 3, giving us the equation 3y = x.
Example of a Two-Step Solution:
Solve for x in the literal equation y = 3x + 4z.
Similarly, x needs to be made the subject of the equation, isolating it to one side of the equation and expressing it in terms of y and z. First, we must remove 4z that is being added to x, and by doing that, we will subtract both sides of the equation with 4z, getting y – 4z = 3x. Then, to remove the 3 that is multiplying to x, we divide both sides of the equation with 3, getting (y – 4z)/3 = x.
Example of a Multi-Step Solution:
Solve for x in the equation y = 3x/4 + 17.
To make x the subject of the equation and express it in terms of y, we isolate the x.
To do that, we first remove 17 that is added to x by subtracting both sides with 17, getting y – 17 = 3x/4.
We then remove the four that is dividing x by multiplying both sides with 4, getting 4y – 68 = 3x.
Finally, divide both sides with 3 to get (4y – 68)/3 = x.
Literal equations are important in finding out the value of unknown variables and are easy to solve when you get the trick. Always remember, make one variable the subject and treat the rest as numbers.