§ 2.2 The Addition Property of Equality. Angel, Elementary Algebra, 7ed 2 Linear Equations A linear equation in one variable is an equation that can be.

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§ 2.2 The Addition Property of Equality

Angel, Elementary Algebra, 7ed 2 Linear Equations A linear equation in one variable is an equation that can be written in the form ax + b = c where a, b, and c are real numbers and a  0. The solution to an equation is the number that when substituted for the variable makes the equation a true statement.

Angel, Elementary Algebra, 7ed 3 Solutions to Equations Example: Is x = – 1 a solution of – 3(x – 3) = – 4x + 3 – 5k? – 3(x – 3) = – 4x + 3 – 5k – 3(( – 1) – 3) = – 4( – 1) + 3 – 5( – 1) (Substitution) – 3( – 4) = (Simplify) 12 = 12 (True) Therefore, x = – 1 is a solution to the equation. ? ?

Angel, Elementary Algebra, 7ed 4 Equivalent Equations Two or more equations with the same solution are called equivalent equations. To ensure that an equation always remains equal, any operation performed on the left side of the equation must also be performed on the right side. Left sideRight side

Angel, Elementary Algebra, 7ed 5 Example: Solve the equation x – 4 = -10. x – 4 = -10 x – = (Add 4 to both sides.) x = -6 Check: (-6) – 4 = -10 Addition Property of Equality If a = b, then a + c = b + c for any real numbers a, b, and c.