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ONE STEP EQUATIONS Addition and Subtraction Expression vs Equation Expression: Examples: • is a PHRASE, a sentence fragment • Cannot be solved • Has no relation symbol Equation: • is a SENTENCE • Has a solution • Has a relation symbol (=) • 2x + 4 • 3(x -5) • 4x + 27 Examples: • 2x + 4 = 10 • 3(x -5) = 7 • 4x + 27 = 20 Equations Ex. 2x + 1 = 9 Solving an equation is finding the value of the variable that makes the sentence true Can x = 5? 2(5) + 1 = 9 10 + 1 = 9 11 = 9 No Can x = 4? 2(4) + 1 = 9 8+1=9 9 = 9 Yes EQUATIONS An equation is like a balance scale because it shows that two quantities are equal. 4 + 2 -2 6 -2 + What you do to one side of the equation must also be done to the other side to keep it balanced. ONE STEP EQUATIONS To solve one step equations, you need to ask three questions about the equation: • What is the variable? • What operation is performed on the variable? • What is the inverse operation? (The one that will undo what is being done to the variable) ONE STEP EQUATIONS Example 1 Solve x + 4 = 12 Variable? x Operation? Add 4 Inverse operation? Subtract What you do to one side of the equation x + 4 = 12 -4 -4 x+0 = 8 x=8 4 must also be done to the other side to keep it balanced. ONE STEP EQUATIONS Check your answer!!!!!! Rewrite original equation substituting our answer for x x + 4 = 12 8 + 4 = 12 12 = 12 Original equation Does our answer make the equation true? Yes ONE STEP EQUATIONS What if my answer was x = 9? Rewrite original equation substituting our answer for x Original equation x + 4 = 12 9 + 4 = 12 Does our answer make the equation true? 13 = 12 No ONE STEP EQUATIONS Example 2 Solve x + 10 = 17 Variable? x Operation? Add 10Inverse Subtract 10 operation? What you do to one side of the equation x + 10 = 17 - 10 - 10 x + 0= 7 x=7 must also be done to the other side to keep it balanced. ONE STEP EQUATIONS Check your answer!!!!!! Rewrite original equation substituting our answer for x x + 10 = 17 7 + 10 = 17 17 = 17 Original equation Does our answer make the equation true? Yes ONE STEP EQUATIONS Example 3 Solve x - 9 = 14 Variable? x Operation? Subtract 9 What you do to one side of the equation x - 9 = 14 +9 +9 x - 0 = 23 x = 23 Inverse operation? Add 9 must also be done to the other side to keep it balanced. ONE STEP EQUATIONS Check your answer!!!!!! Rewrite original equation substituting our answer for x x - 9 = 14 23 - 9 = 14 14 = 14 Original equation Does our answer make the equation true? Yes ONE STEP EQUATIONS Example 4 Solve x - 5 = 11 Variable? x Operation? Subtract 5 What you do to one side of the equation x - 5 = 11 +5 +5 x - 0 = 16 x = 16 Inverse operation? Add 5 must also be done to the other side to keep it balanced. ONE STEP EQUATIONS Check your answer!!!!!! Rewrite original equation substituting our answer for x x - 5 = 11 16 - 5 = 11 11 = 11 Original equation Does our answer make the equation true? Yes TRY: x + 6 = 11 -6 -6 x +0 = 5 x=5 Check: x + 6 = 11 5 + 6 = 11 11 = 11 x-7=5 +7+7 x - 0 = 12 x = 12 Check: x-7=5 12 - 7 = 5 5=5