Addition and Multiplication Property of Equality Addition and Multiplication Property of Equality This is where we start getting into the heart of what algebra is about, solving equations. In this tutorial we will be looking specifically at linear equations and their solutions. In this and the next tutorial, we will start off slow and solve equations that use only one property to make sure you have the individual concepts down. Then, in later tutorials, we will pick up the pace and mix 'em up where you need to use several properties and steps to get the job done. Equations can be used to help us solve a variety of problems. The tutorial is ready when you are. Addition Property of Equality – To move a term from one side of an equation to the other side, add the opposite sign to both sides of the equation. x + 4 = 11 -4 -4 x =7 To move the 4 from the left side of the equation to the right side subtract 4 from both sides of the equation. This leaves you with x on the left side and 7 on the right side. In other words, x = 7. Also, when you are solving an equation always remember to check your answer in the original equation to see if it is the correct answer. Know More About :- Hyperbolic Functions
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Check: x + 4 = 11 (7) + 4 = 11 11 = 11 Replace x with (7) and simplify. This is correct so the answer checks out. Here are some more examples using the Addition Property of Equality: Multiplication Property of Equality: Case 1: To eliminate a number (coefficient) in front of a variable, divide all terms on both sides of the equation by the number. 3x = 12 3x = 12 3 3 x=4 To get the x by itself on the left side of the equation divide both sides of the equation by 3. This leaves you with x on the left side and 4 on the right side. Check 3 x = 12 3(4) = 12 12 = 12 Correct. Case 2: If a variable is already divided by a number, then multiply all terms on both sides of the equation by that number. ase 3: If a variable has a fraction in front of it (fractional coefficient), then multiply all terms on both sides of the equation by the reciprocal of that fraction The x is already divided by 5 , So multiply both sides of the equation by 5. The 5’s cancel on the left leaving x on the left and 20 on the right. Read More About :- Trigonometric Identities
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