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Math: Basic Tutorials : Equation Basics
Equation Basics
An equation is something that contains two quantities separated by an equal sign; the two quantities are equal but are represented differently (e.g. 2+2 = 4). An algebraic equation contains at least one variable that is unknown (e.g. 2+y = 4). This section explains the basics of equations and how to keep them balanced.
Examples & Activity
Examples
Click on the titles below to view each example.
Determine whether x equals 5 is a solution of 4x plus 5 equals 30 minus x.
Line 1: Substitute 5 for x into the equation so it becomes 4 times 5 plus 5 equals 30 minus 5.
Line 2: Multiply to simplify so the equation becomes 20 plus 5 equals 30 minus 5.
Line 3: Add and subtract to simplify so the equation becomes 25 equals 25.
Therefore, x equals 5 is a solution of 4x plus 5 equals 30 minus x.
Determine whether x equals 7 is a solution of 5x equals 50 minus 3x.
Line 1: Substitute 7 for x into the equation so it becomes 5 times 7 equals 50 minus 3 times 7.
Line 2: Multiply to simplify so the equation becomes 35 equals 50 minus 21.
Line 3: Subtract to simplify so the equation becomes 35 does not equal 29.
Therefore, x equals 7 is not a solution of 5x equals 50 minus 3x.
Summary and Worksheet
- Summary: Introduction to Solving Algebraic Equations - PDF - Opens in a new windowThis document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
- Worksheet: Introduction to Solving Equations - PDF - Opens in a new windowThis document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.
Attribution
Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window