Practice sheet 4-1 Go over Homework
4-3 Solving Equations by Adding & Subtracting
Equation An algebraic expression with an equals sign (A complete sentence) 33/x – 2 = 1 x + 3 = 5 4x – 1 = 11
Solution A solution to an equation is any value that makes the equation true. 11 is a solution for 33/x – 2 = 1 2 is a solution for x + 3 = 5 3 is a solution for 4x – 1 = 11
Notice the variable is ALWAYS positive Isolate Notice the variable is ALWAYS positive To get a variable alone on one side of the equation. A = 2 X = 3 - 5 6 = x
Addition Property of Equality When you add the same number/variable to each side of an equation, the two sides remain equal A = B A + C = B + C x - 3 = 5 X -3 + 3 = 5 + 3 -1 = 12 –s -1 +s = 12 – s + s
Subtraction Property of Equality When you subtract the same number/variable to each side of an equation, the two sides remain equal 5(2) = 10 5(2) - 3 = 10 - 3 x + 9 = 5 X +9 - 9 = 5 - 9 -11 = 12 + s -11 - s = 12 + s - s
Ch. 4-3 Solving Equations by Adding and Subtracting To find a solution, isolate the variable, or get it alone on one side. Use the either the addition or subtraction property of equality depending on the operation in front of the number your are trying to move. Example: 8 + x = 10 You want to move the eight to get x by itself. 8 + x = 10 The sign in front of the 8 is positive so -8 -8 subtract 8 from both sides. 0 + x = 2 x = 2 For this section we will be talking about addition and subtraction. Inverse of Addition is ______________ Inverse of Subtraction is _____________ Subtraction Addition
Ch. 4-3 Solving Equations by Adding and Subtracting Steps to solve equation or isolate the variable: Move variable if negative by using the addition property of equality If the number you wish to move is negative use the addition property of equality If the number you wish to move is positive use the subtraction property of equality Simplify Check to see if your answer is correct
Solve Addition Equations Step 2 Use addition property of equality Step 3 Simplify Step 4 Check
Solving Equations by Adding Step 2 Undo subtraction by using the addition property of equality Step 3 Simplify Step 4 Check
Solving Equations by Adding You always want the variable to be positive Step 1 Get rid of negative variable by using addition property of equality Step 2 Get rid of +19 by using subtraction property of equality Step 3 Simplify Step 4 Check
Solving Equations by Subtracting Step 2 Undo addition Step 3 Simplify Step 4 Check
Example 1: Solve each equation below by doing the opposite of the operation shown. a.) p – 1 = -12 b.) -37 = y – 2 c.) a – 9 = 45 d.) b – 2 = -2 e.) a + 15 = 10 f.) x + 9 = -2 g.) 19 + g = 32 h.) -10 = 3 + c +1 = +1 p = -11 +2 = +2 -35 = y or y= -35 +2 = +2 b = 0 +9 = +9 a = 54 -15 = -15 a = -5 - 9 = -9 x = -11 -19 = -19 g = 13 -3 = -3 -13 = c or c = -13
Example 2: For each equation below determine whether -3 is a solution. a.) a + 4 = 7 b.) w – 7 = -10 c.) -1 + c = 4 d.) r + 3 = 0 e.) f.) -3 +4 = 7 1 = 7 No -3 – 7 = -10 -10 = -10 Yes -1 -3 = 4 -4 = 4 No -3 + 3 = 0 0 = 0 Yes 3 +2 = 5 5 = -5 No 3= 3 Yes
Homework Pg 183 Practice Sheet 4-3 all #6-20 even(1 pt for work, 1 for answer) #24 (1 pt for equation, 1 pt for work, 1 pt for answer) Practice Sheet 4-3 all (1 pt for work, 1 pt for answer)
Example 1: Solve each equation below by doing the opposite of the operation shown. a.) p – 1 = -12 b.) -37 = y – 2 a + 15 = 10 f.) x + 9 = -2 g.) 19 + g = 32 h.) -10 = 3 + c -15 = -15 a = -5 - 9 = -9 x = -11 -19 = -19 g = 13 -3 = -3 -13 = c or c = -13
Go over Homework Pg 183 #6-20 even(1 pt for work, 1 for answer) #24 (1 pt for equation, 1 pt for work, 1 pt for answer)
Reteach 4-3 Classwork Homework Practice Sheet 4-3 all (show work)