Solving One-Step Equations

S.W.B.A.T Students will be able to take their knowledge of order of operations and substitution to solve a one step equation

Do Now: Answer the following on a piece of lose leaf a= 5 and b= 2 8a ÷ b

Solving Equations In an equation, the variable represents the number that satisfies the equation To solve an equation means to find the value of the variable that makes the equation true

Process of Solving an Equation The process of solving an equation involves isolating the variable, making it have a coefficient of 1, on one side of the equation

Addition property of equality If an equation is true and the same number is added to each side of the equation, the resulting equivalent equation is also true For any real numbers a, b and c, if a=b, then a + c = b + c

Examples Solve by adding C – 22 + 54 Since we are subtracting 22 from c, we must add 22 to get c by itself. What we do to the left side we must do to the right side C – 22 + 22 = 54 + 22 C = 76 This is the horizontal method, I will show you the vertical method on the board

Check C = 76 C – 22 = 54 76 – 22 = 54 54 = 54

Subtraction Property of Equality If an equation is true and the same number is subtracted from each side of the equation, the resulting equivalent equation is also true For any real numbers a, b and c, if a = b, then a – c = b - c

Examples Solve by subtracting 63 + m = 79 63 is being added to m, in order to isolate the variable we must subtract 63 from each side 63 – 63 + m = 79 – 63 M = 16

Check m = 16 63 + m = 79 63 + 16 = 79 79 = 79

Multiplication Property of Equality If an equation is true and each side is multiplied by the same nonzero number, the resulting equation is equivalent For any real numbers a, b and c, if a = b, then ac = bc

Examples Solve by multiplying Take the fraction being multiplied by the variable and multiply each side by its reciprocal

Division Property of Equality If an equation is true and each side is divided by the same nonzero number, the resulting equation is equivalent For any real numbers a, b and c, if a = b, then

Examples Solve by dividing 39 = -3r Since we want r is being multiplied by -3 and we want r to be by itself we must divide each side by -3 ------- ----- -3 -3 -13 = r

Check -13 = r 39 = -3r 39 = -3 ( -13) 39 = 39