The Basics: Algebraic Equations & Formulas
The Basics:Algebraic Equations & Formulas
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An equation is two expressions connected by an equal sign. In the last module you simplified expressions to find the answer when given the value of the variable. In this module, you will solve equations to find the value of the variable.
A linear equation is an equation that is made up of monomials or polynomials that are of at most degree 1. (This means that the variable does not have a power greater than 1. No x2s in your equations.) A solution to a linear equation is any number that when replaced for the variable in the equation, creates a true statement. That means it makes the equation true on both sides of the equal sign.
Tools for Solving First Degree (Linear) Equations:
Goal: Get “x” (or the variable) alone on one side of the equation and everything else on the other side.
1. Simplify both sides of the equation:
a. Clear parentheses by using the distributive property.
b. Clear fractions by multiplying the entire equation by the LCD (Lowest Common Denominator).
c. Clear decimals by multiplying the entire equation by an appropriate power of 10.
d. Combine like terms, making sure to work with each side of the equation separately.
2. Use the addition/subtraction principle. We can add or subtract a constant to or from both sides of the equation without affecting the solution of the equation.
3. Use the multiplication/division principle. We can multiply or divide both sides of the equation by a constant without affecting the solution of the equation.
4. Check your answer by substituting the answer back into the equation. The beauty of algebra is you can always check if your answer is correct or not.
In the previous module, you solved formulas when given the value of the variables. In this module, you will be solving formulas for a variable. Use the same rules for solving a first-degree equation.
Watch these helpful Khan Academy videos for more information:
Simple Equations Links to an external site.
Solving One-Step Equations Links to an external site.
Solving for a Variable Links to an external site.
Rearrange formulas to isolate specific variables Links to an external site.
Solving Equations with the Distributive Property Links to an external site.
Now move on to the energy technology video demonstrations. When you are ready, take the practice quiz to show what you know. If you think you need more practice, ask your instructor if the optional practice assignments would help you.