One step equations Chapter 2 Section 2.1

Objective Students will solve equations using addition, subtraction, multiplication, and division.

concept Addition Property of Equality If a, b, and c are any real numbers, and a=b, then a + c = b + c and c + a = c + b If the same number is added to equal numbers, the sums are equal

concept Subtraction Property of Equality If a, b, and c are any real numbers, and a=b, then a – c = b – c If the same number is subtracted from equal numbers, the differences are equal

concept Multiplication Property of Equality If a, b, and c are any real numbers, and a=b, then ca=cb and ac = bc If equal numbers are multiplied by the same number, the products are equal

concept Division Property of Equality If a and b are any real numbers, c is any nonzero real number, and a=b, then a = b c c If equal numbers are divided by the same nonzero number, the quotients are equal

concept These properties give you ways to transform an equation into an equivalent equation. An equivalent equation is an equation having the same solution set over a given domain. x – 8 = 17 and x = 25

concept It is often possible to change, or transform, an equation into a simpler equivalent equation by using addition, subtraction, multiplication, and division properties. The goal is to obtain a simpler equation whose solution or solutions can be easily seen.

concept Transformation by Addition Add the same real number to each side of a given equation Transformation by Subtraction Subtract the same real number from each side of a given equation

concept Transformation by Multiplication Multiply each side of a given equation by the same nonzero real number Transformation by Division Divide each side of a given equation by the same nonzero real number

example x + 5 = 9 x – 2 = 7

example -5 = x + 13 -8 + x = -8

example 6x = 222 8 = -2/3x

example x/3 = -5 1/4x = 6 ¼

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