chapter 3 – solving linear equations 3.1 – solving equations using addition and subtraction

Chapter 3 – Solving Chapter 3 – Solving Linear EquationsLinear Equations

3.1 – Solving Equations Using 3.1 – Solving Equations Using Addition and SubtractionAddition and Subtraction


Today we will be learning about:Today we will be learning about: Solving linear equations using addition Solving linear equations using addition

and subtractionand subtraction

Using linear equations to solve real-life Using linear equations to solve real-life problemsproblems


You and a friend are walking down You and a friend are walking down Main Street and you find $10. You Main Street and you find $10. You put it in your pocket with the rest of put it in your pocket with the rest of your money. At King’s later that day, your money. At King’s later that day, you go to checkout and see that you you go to checkout and see that you have $28. How much money did you have $28. How much money did you have have beforebefore you found the $10? you found the $10?


When solving equations, our goal is to get When solving equations, our goal is to get the variable by itself. the variable by itself. We need to get the variable on one side of the We need to get the variable on one side of the

equal sign.equal sign. We do this by adding and subtracting We do this by adding and subtracting

numbers from BOTH SIDES of the equation numbers from BOTH SIDES of the equation to keep the equation balanced.to keep the equation balanced. These are called These are called EQUIVALENT EQUATIONSEQUIVALENT EQUATIONS

To get the variable by itself, we do the To get the variable by itself, we do the INVERSE OPERATIONINVERSE OPERATION Operations that undo each otherOperations that undo each other


EQUIVALENT EQUATIONSEQUIVALENT EQUATIONS Adding the same number to each sideAdding the same number to each side

ORIGINAL: ORIGINAL: xx – 3 = 5 – 3 = 5 Add 3 to both sidesAdd 3 to both sides

EQUIVALENT: EQUIVALENT: xx = 8 = 8 Subtracting the same number from each Subtracting the same number from each

sideside ORIGINAL: ORIGINAL: xx + 6 = 10 + 6 = 10

Subtract 6 from both sidesSubtract 6 from both sides EQUIVALENT: EQUIVALENT: xx = 4 = 4


EQUIVALENT EQUATIONSEQUIVALENT EQUATIONS Simplifying one or both sidesSimplifying one or both sides

ORIGINAL: ORIGINAL: xx = 8 – 3 = 8 – 3 EQUIVALENT: EQUIVALENT: xx = 5 = 5

Interchange the sidesInterchange the sides ORGINAL: 7 = ORGINAL: 7 = xx EQUIVALENT: EQUIVALENT: xx = 7 = 7


Example 1Example 1 Solve the following equations:Solve the following equations:

xx – 9 = -17 – 9 = -17

-11 = -11 = nn – (-2) – (-2)

5 + 5 + xx = -3 = -3


Example 2Example 2 The normal high temperature in January The normal high temperature in January

in Oley, Pennsylvania is 36in Oley, Pennsylvania is 36°F and the °F and the normal low is 17°F. How many degrees normal low is 17°F. How many degrees apart are the high and low apart are the high and low temperatures?temperatures?


Example 3 Match the real-life

problem with the equation.

1. x + 7 = 9

2. x – 2 = 7

3. 9 – x = 7

a. You have x dollars and your friends repays you the $7 he owes you. You now have $9. How much did you originally have?

b. The temperature was x °F. It fell 2°F and is now 7°F. What was the original temperature?

c. A 9 foot post extends x feet below the ground and 7 feet above ground. What is the length x buried below the ground?


HOMEWORKHOMEWORK

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#22 – 40 even, 45 – 49#22 – 40 even, 45 – 49

chapter 3 – solving linear equations 3.1 – solving equations using addition and subtraction

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