3/26/2023 0 Comments Mathmod equations![]() Should we begin by dividing both sides by 3? Or would it be better to add 7 to both sides?Īnswering this question can be difficult if you don't have a strategy. Whenever you have an equation to solve, it is helpful to have a strategy to help you get started. Some equations will look like the ones above, but others will be more complicated to solve. Solve the following equations and see if you can determine a pattern for the value you multiply or divide to both sides of the equation (solutions are on the last page of this guide). Original equation: 8 y = 88 Divide both sides by 8: 8 y 8 = 88 8 Equivalent equation: y = 11Ĭheck for Understanding #2: The Multiplication Property of Equality The Multiplication Property of Equality also applies to dividing both sides of the equation: For any real numbers a, b, and c, if a = b, then a c = b c The Addition Property of Equalityīy multiplying both sides of the equation by 4, we can create an equivalent equation, r = 24, that makes the solution clear. We'll use the idea of equivalent equations in the Addition Property of Equality, and later the Multiplication Property of Equality. Let's first cover the addition property of equality. This is the equation (solution) we want to find because it is the easiest to read and tells us the solution to the equations. Why is this? Plugging in x = 16 into equation makes each equation true. They are, but the most valuable equivalent equation would be the one that reads x = 16. Let's consider two equations:Īre 0.05x - 0.2 = 0.6 and 0.5x = 8 equivalent equations? But not all equivalent equations are so obvious. You can probably look at this example and determine the value of x that makes that statement true. Placing x = 3 into the equation x + 4 = 7, 3 + 4 = 7, and 3 = 3. In both, if the variable x is 3, the equation is true. So how do we know these two equations are equivalent to each other? A solution to an equation is also an equivalent equation-that is, the solution is equivalent to the original equation.įor example, the equations x + 4 = 7 and x = 3 are equivalent. You might think of this as solving for the "answer," or finding the solution. When solving an equation, the goal is to create equivalent equations-the original equation and its solution. Equivalent Equations: Two (or more) equations that have the same solution. ![]() ![]() Solution: The value of the variable (such as x, y, and z) that makes an equation true.The coefficient is the number that is being multiplied by the variable.Letters are most often used as variables, such as x, y, and z. A variable is a symbol that represents an unknown quantity.When reading through these vocabulary terms, consider the equationĪnd use the figure below – Parts of an Equation – as a guide to understanding how these vocabulary terms are used. Let's start by looking at a few key terms we can use to understand different parts of an equation. Equations are typically designated by the equal symbol (=). An equation is a statement that two quantities are equal. The Multiplication Property of Equalityīefore we begin solving equations, we should understand what an equation is.Justice Involved Students Pathway Program.Extended Opportunity Programs and Services.
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