ONE STEP EQUATIONS Addition and Subtraction

Expression vs Equation Examples: 2x + 4 3(x -5) 4x + 27 is a PHRASE, a sentence fragment Cannot be solved Has no relation symbol Equation: Examples: 2x + 4 = 10 3(x -5) = 7 4x + 27 = 20 is a SENTENCE Has a solution Has a relation symbol (=)

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)

/ / x + 4 - 4 - 4 x + = 8 x = 8 ONE STEP EQUATIONS Example 1 Solve x + 4 = 12 Inverse operation? Variable? x Operation? Add 4 Subtract 4 x + 4 = 12 x + 4 / must also be done to the other side to keep it balanced. What you do to one side of the equation / - 4 - 4 x + = 8 x = 8

Check your answer!!!!!! 12 = 12 ONE STEP EQUATIONS x + 4 = 12 Rewrite original equation substituting our answer for x Original equation x + 4 = 12 8 + 4 = 12 Does our answer make the equation true? 12 = 12 Yes 

13 = 12 ONE STEP EQUATIONS What if my answer was x = 9? x + 4 = 12 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

/ / x + 10 - 10 - 10 x + = 7 x = 7 ONE STEP EQUATIONS Example 2 Solve x + 10 = 17 Inverse operation? Variable? x Operation? Add 10 Subtract 10 x + 10 = 17 x + 10 / must also be done to the other side to keep it balanced. What you do to one side of the equation / - 10 - 10 x + = 7 x = 7

Check your answer!!!!!! 17 = 17 ONE STEP EQUATIONS x + 10 = 17 Rewrite original equation substituting our answer for x Original equation x + 10 = 17 7 + 10 = 17 Does our answer make the equation true? 17 = 17 Yes 

/ / x - 9 + 9 + 9 x - 23 = x = 23 ONE STEP EQUATIONS Example 3 Solve x - 9 = 14 Inverse operation? Variable? x Operation? Subtract 9 Add 9 / x - 9 = 14 x - 9 must also be done to the other side to keep it balanced. What you do to one side of the equation / + 9 + 9 x - = 23 x = 23

Check your answer!!!!!! 14 = 14 ONE STEP EQUATIONS x - 9 = 14 Rewrite original equation substituting our answer for x Original equation x - 9 = 14 23 - 9 = 14 Does our answer make the equation true? 14 = 14 Yes 

/ / x - 5 + 5 + 5 x - 16 = x = 16 ONE STEP EQUATIONS Example 4 Solve x - 5 = 11 Inverse operation? Variable? x Operation? Subtract 5 Add 5 / x - 5 = 11 x - 5 must also be done to the other side to keep it balanced. What you do to one side of the equation / + 5 + 5 x - = 16 x = 16

Check your answer!!!!!! 11 = 11 ONE STEP EQUATIONS x - 5 = 11 Rewrite original equation substituting our answer for x Original equation x - 5 = 11 16 - 5 = 11 Does our answer make the equation true? 11 = 11 Yes 

TRY: x + 6 = 11 x + 6 x - 7 = 5 x - 7 / / - 6 + 7 / + 7 / - 6 x + 5 x 12 = = x = 5 x = 12 Check: Check: x + 6 = 11 x - 7 = 5 5 + 6 = 11 12 - 7 = 5 11 = 11 5 = 5  