more equations solving multistep equations. some equations may have more than two steps to complete....

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Solving Multistep EquationsSolving Multistep Equations

Some equations may have more than two steps to complete. You may have to

simplify the equation first by combining like terms or even remove fractions to

make solving easier.

Samantha and Rebecca want to rent sports equipment at the city park. Samantha wants to rent inline skates, and Rebecca wants to rent a motor scooter.

How would you write an equation and solve the problem to find the total cost for a specified number of hours.

Let’s take a look at how you would solve this problem.

Here is the cost for each of the activities the girls would like to rent. Let’s look at

each individually and then together.

Inline Skates$3.00 plus $1.50/hour

c = 3 + 1.50x

c = individual costx = number of hours

rental

Motor scooter$10.00 plus

$2.75/hour

c = 10 + 2.75x

c = individual costx = number of hours

rental

Independent variable

Dependent variable

constant

Independent variable

Dependent variable

constant

Combined cost (C)Use the equation C = 3 + 1.50x + 10 + 2.75x to answer each of the following

questions.C = 4.25x + 13

• How much would Samantha and Rebecca pay for 2 hours’ rental?

• How much would Samantha and Rebecca pay for 3 hours’ rental?

• If their total rental cost is $38.50, for how many hours did they use the equipment?

Multistep EquationsMultistep EquationsMultistep EquationsMultistep EquationsEquations with Equations with Like TermsLike Terms

Equations that contain Equations that contain FractionsFractions

Equations with Equations with variables on both variables on both sidessides

Important!To solve multistep equations, first clear fractions and combine like terms. Then

add or subtract variables to both sides so that the variable is on one side only.

Multistep equations

STEP 1: Clear fractions

STEP 2: remove parenthesis

STEP 3: move all variables to one side

of the equation.

Solving equations containing like terms

8x + 6 + 3x – 2 = 37 11x + 4 = 37 Combine like terms

11x + 4 – 4 = 37 – 4 Subtraction Property of Equality

11x = 33 Division Property of Equality

11 11 x = 3

Remember to keep your equal signs lined up to prevent you from making a mistake. On the next slide we will check our answer by substituting for x.

Check your answer by substituting for x

8x + 6 + 3x – 2 = 378(3) + 6 + 3(3) – 2 = 37 Substitute 3 for x

24 + 6 + 9 – 2 = 37 Combine like terms

37 = 37 ? True

Solve:

1) 8d – 11 + 3d + 2 = 13

2) 8x – 3x + 2 = -33

3) 2y + 5y + 4 = 25

4) 4x + 8 + 7x -2x = 89

5) 30 = 7y – 35 + 6y

Solving equations that contain fractions

5n + 7 = -3 Multiply both side by 4 to clear fractions

4 4 44 · 5n + 7 = -3 · 4 Multiply both sides by 4, Multiplication Property of Equality

4 4 4 5n + 7 = -3 Subtract 7 from both sides, Subtraction Property of Equality

5n + 7 – 7 = -3 – 7 5n = -10 Divide both sides by 5, Division Property of Equality

5 5 n = - 2 Remember to go back an substitute for n

Solve:

1) 4 – 2p = 6 5 5 5

2) 9z + 1 = 2 4 4 4

3) x + 2 = 5 2 3 6

Solving equations with variables on both sides is similar to solving an equation with

a variable on only one side.

You can add or subtract a term containing a variable on both sides of an equation.

2a + 3 = 3a2a – 2a + 3 = 3a – 2a Subtract 2a from both sides.

3 = a

Remember to keep equal (=) signs lined up to prevent errors. Always go back and check each equation by substituting the solution into the original equation.

Moving terms is just like moving a single number, you use the

Properties of Equality.

Solving equations with variables on both sides.

4x – 7 = 5 + 7x4x – 4x -7 = 5 + 7x -4x Subtract 4x from both sides.

-7 = 5 + 3x -7 -5 = 5 – 5 + 3x Subtract 5 from both sides.

-12 = 3x -12 = 3x Divide both sides by 3.

3 3 -4 = x Remember go back and substitute for x.

Remember, you can move a whole term.

Solve:

1) 5x + 2 = x + 6

2) 4y – 2 = 6y + 6

3) 4(x - 5) + 2 = x + 3

4) 4x – 5 + 2x = 13 + 9x – 21

5) 8x – 3 = 15 + 5x

Both figures have the same perimeter. What is the perimeter.

Remember how to find the perimeter

of a polygon?Well, these

two perimeters

are the same.

Write an equation and solve the following problem.

Sam and Ted have the same number of baseball trading cards in their collection. Sam has 6

complete sets plus 2 individual cards, and Ted has 3 complete sets plus 20 individual cards.

How many cards are in a complete set?

Find three consecutive whole numbers such that the sum of the first two numbers equals the third number. Hint: Let n represent the first

number.)

Solve and check.

1) 6x + 3x – x + 9 = 33

2) -9 = 5x + 21 + 3x

3) 4 – 2p = 6 5 5 5

4) y – 3y + 1 = 1 2 8 4 2

5) 5y – 2 – 8y = 31

6) 28 = 10a – 5a – 2

7) x + 2 = 5 2 3 6

8) 5n – 2 – 8n = 31