Equations

Think of this equation as a balance scale. 1) Solve r + 16 = -7 Think of this equation as a balance scale. r + 16 -7 = Whatever you do to one side has to be done to the other to keep it balanced!

1) Solve r + 16 = -7 To solve, you must get the variable by itself. What number is on the same side as r? 16 To get r by itself, we must undo the “add 16”. What is the opposite of addition? Subtract 16

Inverse Operations (opposites) Addition / Subtraction Multiplication / Division Powers (Exponents)/ Roots Undo opposite of the order of operations. PEMDAS

SOLVING EQUATIONS COPY and STUDY VERY IMPORTANT 1 SOLVING EQUATIONS COPY and STUDY VERY IMPORTANT 1. What symbol splits the equation into 2 sides? 2. Are there any ( ) on either side? a. If there are rewrite without ( ) using the distributive property or clearing a fraction using the reciprocal 3. How many terms are on each side? 4. Can either side be simplified further What types of terms are on each side?(variable terms, Numerical terms) Are there any like terms on either side that can be combined !! Goal 1: Use the inverse(opposite) operations addition and subtraction : Get a single term on each side Variable term = Numerical Term Or Numerical term = Variable Term Goal 2: Use the inverse operations multiplication and division to get a coefficient of 1 Variable being multiplied example 3x you would divide both sides by 3 Variable being divided example you would multiply both sides by 6 Variable with fractional coefficient multiply by the reciprocal Example you would multiply both sides by

since it is equal to zero the Additive Identity Please Copy Y Y B G = -1 + = Green means GO it goes away since it is equal to zero the Additive Identity B = 1 -x -x x + = = -1x x = 1x

8 = m - 3

-q + – 15 = -7

-x - (-2) = 1

Check your answer by substituting your answer back into the problem -3v = -129 Check your answer by substituting your answer back into the problem USE THE STO> Button

4) Solve You don’t like fractions? Let’s get rid of them!  “Clear the fraction” by multiplying both sides of the equation by the denominator Or by using the reciprocal!

How could you clear the fraction????

Check your answer by substituting your answer back into the problem USE THE STO> Button

To solve two-step equations, undo the operations by working backwards. Recall the order of operations as you answer these questions. Dividing by 2 Subtracting 3 Example: Ask yourself, What is the first thing we are doing to x? What is the second thing? To undo these steps, do the opposite operations in opposite order.

Worksheet 2.1

Addition Property of Equality

Division Property of Equality Subtraction Property of Equality

Multiplication Property of Equality

-5n – 12 = 31

6b + 4 = -2

7t – 4 – 3t = 2

10 = -4(3t – 2)

n + 6(n – 2) = 8

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2x + 3 = 4x - 6

3(x – 2) = 4(5x + 2)

2x – 3 = 4(3x + 2)

5(x – 2) = 5x – (7x + 3)

-2x -2x 5 = -3 This is never true! No solutions Special Case #1 6) 2x + 5 = 2x - 3 -2x -2x 5 = -3 This is never true! No solutions Draw “the river” Subtract 2x from both sides Simplify

Infinite solutions or identity Special Case #2 7) 3(x + 1) - 5 = 3x - 2 3x + 3 – 5 = 3x - 2 3x - 2 = 3x – 2 -3x -3x -2 = -2 This is always true! Infinite solutions or identity Draw “the river” Distribute Combine like terms Subtract 3x from both sides Simplify

Worksheet 2. 2 Write an equation that models the situation Worksheet 2.2 Write an equation that models the situation. Then, solve the problem. 25) A rectangular trampoline has an area of 187 square feet. The length of the trampoline is 17 feet. What is its width?

26) The van used to transport patients to and from rehabilitation facility is equipped with a wheelchair lift. The maximum lifting capacity for the lift is 300 pounds. The wheelchairs used by the facility weigh 55 pounds each. What is the maximum weight of a wheelchair occupant who can use the lift?

27) A dance academy charges $24 per class and a one-time registration fee of $15. A student paid a total of $687 to the academy. Find the number of classes the student took.

28) Jenny has a job that pays her $8 per hour plus tips (t) 28) Jenny has a job that pays her $8 per hour plus tips (t). Jenny worked for 4 hours on Monday and made $65 in all. How much money did Jenny make in tips on Monday?

14 + 3n = 8n – 3(n – 4) x – (2x + 20) = 12

4(3m + 4) = 2(6m + 8) 1 3 + 2 3 𝑚= 2 3 𝑚− 2 3