Solving Two step equations Using addition, subtraction, multiplication and division

Review 1. x/3 =5 2. y-2=17 3. 15=12+ x 4. 12r=6 5. 14n=6 6. x-9+3=4

Two Step Equations How do we solve: Two step equations combine both kinds of one step equations that we have looked at. Addition or subtraction Multiplication or division How do we solve: Step one= add or subtract Step two= multiply or divide

Example 2x+5=25 Step one: subtract 5 from both sides Step two: divide by 2 on both sides 2x=20 x= 10 -5 -5 2x=20 2 2

Step one: isolate the term containing the variable 2x + 5 = 15 -5 = -5 When we solve two step equations, we want to get the term with the variable alone on one side of the equal sign. Then we want to get the variable alone. 2x + 5 = 15 Step one: isolate the term containing the variable 2x + 5 = 15 -5 = -5 2x = 10 Step two: isolate the variable itself (1/2)(2 x =10)(1/2) x= 10(1/2) x=5 * Remember: Multiplying by ½ is the same thing as dividing by 2 (Inverse Property)

Practice 3x + 5 = 17 x – 6 = 10 2 2t + 12 = 54 19 = 4 + 5k x = 4

Special Case In certain cases, you have to multiply or divide first. Ex. 5 = x+ 2 3 You have to multiply by 3 first, then subtract 2. 15 = x+2 x = 13

Equations with Integers -3x = 12 17 – y = 9 r = -s 3

Positive and Negative Numbers We solve equations with integers the same way we would solve other equations. The only difference is that we need to pay attention to integer rules. Ex. -3x = 12 To get x alone, we have to divide by (-3). -3x = 12 -3 -3 x = -4 why is it negative?

Examples: Addition and Subtraction -5 + y = -7 r + 6 = 4 -12 = k + 4 y = -2 r = -2 k = -16

Examples: Mult. And Division 17 = b -3 p = -2 m = 2.095 b = -51

Two Step Examples -4x + 3 = -13 6 – y = -4 -3 -3 -4x = -16 6 – 1y = -4 -3 -3 -4x = -16 -4 -4 x = 4 6 – y = -4 When a variable is alone, there is a 1 before it! 6 – 1y = -4 -6 -6 -1y = -10 y = 10 -1 -1