Solving Equations Review

Solving Equations Review

​What is an equation?

An Equation is a statement that states that two quantities are equal.

​Equation	​ Not an equation
​ 2x = 12	​ 3(x-5) + 6x
​3x - 5 = 22	​2x + 1
​3(x-4) = 2x + 11	​5x

Multiplication and division are inverse operations for each other. You use division to "undo" multiplication and multiplication to "undo" division.

​Multiplication and Division

Addition and subtraction are inverse operations for each other. You use addition to "undo" subtraction and subtraction to "undo" addition.

​Addition and Subtraction

Inverse Operations

Examples of One-Step Equations

Match

Match the equation with the inverse operation needed to solve it.

• 4x = 16

• 16 = x/4

• x-4 = 16

• x+4 =16

divide by 4

multiply by 4

add 4

subtract 4

• divide by 4

• multiply by 4

• add 4

• subtract 4

Multiple Choice

-5x = 25

• x = 20
• x = -20
• x = -5
• x = 5

Multiple Choice

19  + a  =  -50

• a = -950
• a =  -69
• a = -31
• a = -50/19

Multiple Choice

m - 8 = -5 

• m = 13
• m = -13
• m = 3
• m = -3

Multiple Choice

• x = 20
• x = 7
• x = 10
• x = 3

Multiple Choice

How would you solve this equation: 9x = 153 ? 

• multiply both sides by 9
• divide both sides by 9
• add 9 to both sides
• subtract 9 from both sides

Multiple Choice

Which equation has a = 5 as the solution?

• a + 15 = 10
• 2a = 5
• 2a = 10
• a - 15 = 10

Multiple Choice

x - 62 = 123
How should you show your work to solve the equation?

• Add 62 to each side. 
• Subtract 62 from each side.
• Multiply each side by 62.
• Add 123 to each side.

Draw

BRAIN BREAK:

Beach or Mountains??

Draw your favorite place to visit.

Examples of Two-Step Equations

Multiple Choice

What is the first step to solve this equation:
11 - 3x = 44

• Add 3 to both sides
• Subtract 11 from both sides
• Add 11 to both sides
• Divide 3 on both sides.

Multiple Choice

The steps in solving 5b - 6 = 24 are: 

• Add 6 to both sides and divide both sides by 5
• Add 6 to both sides and multiply both sides by 5
• Subtract 6 from both sides then multiply both sides by 5
• Subtract 6 from both sides then divide both sides by 5

Multiple Choice

Solve

• x = 55
• x = 60
• x = 17.5
• x = 45

Fill in the Blanks

3a + 4 = 31

Multiple Choice

What operation would you perform first and then second when solving for m in the following equation? 10 + 7m = 17

• subtract 10, divide by 7

• divide by 7, subtract 10

• multiply by 7, add 10

• add 10, multiply by 7

Multiple Choice

True or False: In order to solve the equation below, you would add 6 to each side then multiply by -8 on each side.

$$\frac{g}{-8}\ -6\ =\ -12$$  

• true

• false

Multiple Choice

What operations should be done to both sides to isolate the variable x?

• Step 1: + 2
  Step 2: $$\times$$ 3

• Step 1: $$+$$ 2
  Step 2: $$\div$$ 6

• Step 1: $$\div$$ 6
  Step 2: $$-$$ 2

• Step 1: $$-$$ 3
  Step 2: $$\div$$ 6

Multiple Choice

Solve: 3x + 7 = -8

• 5

• -5

• -12

• -18

Multiple Choice

Q. 

Find the error in the problem.

• Should have added 19 to -1.

• Should have subtracted 3k instead of adding 3k to both sides.

• Should have gotten k = 20 since two negatives make a positve.

• There is no error.

Multiple Choice

What is a basketball hoops diameter and height?

• Diameter= 18 inches Height= 10 feet
• Diameter= 10 inches Height= 7 feet
• Diameter= 15 inches Height= 12 feet
• Diameter= 17 inches Height= 9 feet

Multiple Choice

The Line Labeled with a number 5 is the ___________ .

• Sideline
• Free Throw line
• Mid Court line
• Baseline

Multiple Choice

How many field players does each team have in a basketball game?

• 3

• 7

• 5

• 4

Dropdown

James Naismith ​was a​

Select answer

. He ​ invented​ basketball in ​

Select answer

.

What are like terms?

​For example 6x-4+3-5x

Like terms are 6x-4+3-5x

The sign in front of the term is crucial!!!​

Like terms are terms that have the same variables and raised to the same powers (same exponent)

How do we combine like terms?

​For example 6x-4+3-5x

Like terms are 6x-4+3-5x

Add the terms ​6x+(-5x)+(-4)+(+3)

The sign in front of the term is crucial!!!​

1. Use circles, underlines, or a highlighter to identify like terms INCLUDING THE SIGN IN FRONT OF IT

2. Combine the terms by adding like terms together - DO NOT USE INVERSE OPERATIONS

Multiple Choice

Which answer choice contains ALL like terms?

• -4x, 2x, 3x
• -4x, 2, 3y
• 4x², 2x
• 14, 4x

Multiple Choice

Identify Like Terms
4r+2-6+2r

• 4r and 2r
• 2 and 6
• 4r and 2r,
   2 and 6
• 4r and 2r,
   2 and -6

Multiple Choice

Combine like terms: 2r + 2 + 5r - 2 + r 

• 8r 
• 8r - 4 
• 12r 
• 7r + 4 + r 

For the problem 2(3x+1)

• 2 should be multiplied by 3x and 1

• 2(3x) means you multiply the numbers in front of the x

• 2 should then be multiplied by one

• since 6x has an x in it and 2 does not they can't be added.

​2(3x+1) = 6x+2

​Distributive Property:
Multiply the term outside the parentheses by each term inside the parentheses.

Multiple Choice

Distribute: 2(4X-7)

• 8x-14
• 8x-7
• 6x+7
• 8x+14

Multiple Choice

Distribute: 7(y+9)

• 7+9
• 7y+63
• -7y-63
  -7y+63
• 7x+63

Multiple Choice

Distribute: -1(3v - 8)

• -3v-8

• 3v-8

• -3v+8

• 6v+8

Multiple Choice

Distribute

9(x - 5)

• 9x + -45

• 9x + 5

• 9x + 14

• 9x + 45

​Steps to Solving a Multi-Step Equation

• Fractions? Remove any fractions outside of any parentheses by multiplying by the denominator​

• Parentheses? Distribute

• Is each side simplified? ​Combine like terms on each side (DO NOT use inverse operations)

• ​Do I have variables on both sides of the equation? Get the the variables to one side using inverse operations. (You should have a one or two-step equation after this step)

• ​Isolate the variable: add or subtract on both sides, then multiply or divide

Multiple Choice

2 (n + 5) = -2 The first step in solving the following equation is ____________

• add five to both sides
• distribute 2 to all terms in the parenthesis
• add 2

Multiple Choice

What should be the first two steps to solve this equation?

2x +4(3x + 6) = 90

• combine 2x and 3x and then distribute the 4.

• subtract 6 from both sides and then divide by 4

• distribute the 4 and then combine like terms by addition

• combine 2x and 3x and then subtract 6 from both sides

Multiple Choice

What is the error?

• Subtracting 1 from both sides

• Dividing by 6 on both sides

• 3(2x+1) equals 6x +1

• x equals 3/4

Multiple Choice

What is the next step to solve this equation?
3x + 6 = 10 + 7x

• Add 6 to both sides of the equation

• Add 10 to both sides of the equation

• Add 7x to both sides of the equation

• Subtract 7x from both sides of the equation

Multiple Choice

What is the error?

• Adding 2x to 3x

• Subtracting 5 from both sides

• Adding 2x to -2x

• Dividing by 5 on both sides

Multiple Choice

4x - 3 = -2x + 4
6x - 3 = 4
6x = 7
x = 7/6

• There is no error
• They should have subtracted 2x
• They should have subtracted 3
• it should be 6/7

Reorder

Reorder the following steps to solve for x

5(x-4) + 3x -1 = 10x -2

• Combine like terms

• Distribute the 5

• Subtract 8x

• Add 3

• Divide by 2

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

Is the solution below correct?
5d = 2d - 18
-2d   -2d
3d = -18
d = 6

• Yes
• No

Multiple Choice

Find the Error
What error did the student make when solving the equation:
5x + 6 =  66
5x +6 - 6 = 66 -6
5x = 60
5*5x= 60*5
x = 300

• The student subtracted 6 from both sides instead of adding
• Student multiplied by 5 instead of dividing by 5
• Student got the wrong answer when subtracting 66-6
• The student did not correctly eliminate the variable from one side of the equation

Multiple Choice

Which is the correct order in which to solve multi-step equations?

• Get Rid of Fractions

  Distribute

  Combine like terms

  Get the variable on one side by add or subtracting

  Divide or multiple

• Add or subtracting

  Distribute

  Combine like terms

  Divide or multiple

• Add or subtracting

  Divide or multiple

  Distribute

  Combine like terms

Multiple Choice

Which step cannot be performed first when solving the equation

5 - 2(x - 7) = x + 1 + 3x

• Distributing -2 to (x - 7)

• Combining x and 3x

• 5 - 2

Multiple Choice

What is the first step you should take to solve this problem?

1 + 4n - 6n = 1 - 8n

• subtract 8n to both sides

• combine like terms 4n, -6n and -8n to get -10n

• combine the like terms 4n + -6n to get -2n

• add 1 to both sides

• combine like terms 4n and -6n to get 10n

Multiple Choice

Jacob solved the following equation using the steps shown.

Step 1 5x + 9 = 2x - 3

Step 2 3x + 9 = -3

Step 3 3x = -12

Step 4 x = -4

What operation did he perform to get from Step 1 to Step 2?

• Subtracted 2x from both sides of the equation

• Subtracted 9 from both sides of the equation

• Multiplied both sides of the equation by 3

• Added -3 to both sides of the equation

Multiple Choice

5 + 2(n + 1) = 2n
Bill says the first step is to add and get
7(n + 1) = 2n

• Bill is correct
• Bill is wrong; he should have distributed the 2 first.
• Bill is wrong; he should have subtracted 5 from both sides first.
• Bill is wrong; he should have divided by 2 firat.

Multiple Choice

Solve: 5(x - 3) + 2x = 20

• x = 4

• x = 5

• x = -1

• x = -5

Multiple Choice

Solve the equation:

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

• 4

• 3

• 2

• 1