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.
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.
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