Steps to Solve Algebraic equations (Crit A)

Solving Equations Assessment

Monday, March 6

• Inverse Operations

• Substitution

• Solving Equations

• ​Equations Word Problems

• Two-Step Equations

Algebra is fun!!!!!​

We use inverse operations to solve equations. We must isolate the variable by "doing the opposite". ​

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​Inverse Operations

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Multiple Choice

What operation is the inverse of subtraction?

• division

• addition

• multiplication

• exponents

Multiple Choice

What operation would you use to solve the equation: $$\frac{p}{100}=2$$  

• division

• multiplication

• exponents

• subtraction

​ Solving Equations

Multiple Choice

Solve the equation:

w - 14 = 6

• w = 8

• w = 20

• w = 2 1/2

• w = -8

Multiple Choice

Solve the equation: $$\frac{n}{7}=7$$  

• n = 1

• n = 14

• n = 49

• n = 42

Multiple Choice

Solve the equation:

3b = 18

• b = 6

• b = 21

• 54

• b = 15

Algebraic Rules

To describe a pattern using an algebraic rule, choose variables to represent the term number and the number in the pattern.

​Here, we will use x for the term number and y for the number in the pattern. Since we multiply the term number by two to get the number in the pattern, the rule is 2x = y.

Multiple Choice

The table shows how much money (A) Bev has saved each month (m). Which algebraic rule represents the situation:

• m = 12A

• A = 12m

• A = m + 12

• m = A + 1

Multiple Choice

The table represents the amount of chocolate chips in grams (g) needed to bake a batch of cookies (b). Which algebraic rule represents the situation:

• g = 75b

• g = b + 75

• b = g/4

• b = g/2

​Two-Step

Equations Example

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​Solving Two-Step Equations

1. First, add or subtract both sides of the equation by the same number.

2. Second, multiply or divide both sides of the equation by the same number.

Multiple Choice

Solve the equation: 2x + 10 = 16

• x = 42

• x = 3

• x = 4

• x = 18

Multiple Choice

Solve the equation: $$\frac{h}{11}-\ 5\ =\ 2$$  

• h = 17

• h = 77

• h = 10.5

• h = 55

​Solving Equations

​GOAL: isolate the variable (get the variable by itself)

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​STEPS TO SOLVE:

​1. Use inverse operations 

• Addition and subtraction

• Multiplication and division 

2. Whatever operation you do to one side, you must do to the other side

3. Check your answer by plugging the x-value back in to the original equation

Multiple Select

What are the two basic rules for solving algebraic equations?

• Whatever you do to one side of the equal sign, you must copy and do on the other side of the equal sign

• Negative signs can be ignored

• Always start on the left side, regardless of where the variable is

• Always use inverse operations

Multiple Choice

What is one difference between an algebraic expression and an equation?

• Algebraic expressions do not have variables, but equations do have variables

• Expressions and equations are not different

• Expressions do not have an equal sign and equations need to have an equal sign

• Expressions need to have an equal sign and equations do not have an equal sign

Multiple Choice

Solve:

2x = -16

• -8

• $$\frac{1}{8}$$

• 8

• $$\frac{-1}{8}$$

Multiple Choice

Solve:

y + 9 = -10

• 1

• -1

• 19

• -19

Multiple Select

Which of the following are basic rules used for solving algebraic equations?

• Do the same thing to both sides of the equation

• Consolidate the variable

• Ignore all rules and take a guess

• Isolate the variable

​Writing Expressions and Equations from Word Problems

​*Look for clue words that help you determine which operation should be used.

​*Phrases such as, "equals", "is", and "is equal to" indicate an equation rather than an expression

Multiple Choice

twice a number plus 8

• 2 + 8a

• 8 - 2a

• 2a + 8

• $$\frac{a}{2}$$ + 8

Multiple Choice

The sum of a number k and a number j reduced by 10

• k + j - 10

• (k + j) + 10

• (k - j) - 10

• (k + j) - 10

Multiple Choice

Which equation has x = 5 as the solution?

• x + 15 = 10
• 2x = 5
• 2x = 10

Multiple Choice

x + 12 = 20

• x = 32
• x = -32
• x = 8
• x = -8

Multiple Choice

5m = 10  solve for m

• 50
• 15
• 5
• 2

Multiple Choice

Solve for the missing variable:

• m = 5
• m = 1/5
• m = 25
• m = 55

Multiple Choice

x - 16= 15

• 2

• 0

• -1

• 31

Multiple Choice

Solve the equation:

5x = 25

• x = 20

• x = -20

• x = -5

• x = 5

Multiple Choice

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

• multiply by 9 on both sides

• divide by 9 on both sides

• add 9 to both sides

• subtract 9 from both sides

Multiple Choice

m - 5 = 10

• -15

• 15

• -5

• 5

Multiple Choice

What is the inverse operation of division?

• Division
• Multiplication
• Addition
• Subtraction

Multiple Choice

What is the inverse operation of subtraction?

• addition

• subtraction

• multiplication

• division

Multiple Choice

What is the correct step to solve for the variable?
15 = m - 5

• add 15 to both sides
• add 5 to both sides
• subtract 15 from both sides
• subtract 5 from both sides

Multiple Choice

What is the inverse operation of division?

• Division
• Multiplication
• Addition
• Subtraction

Multiple Choice

x ÷ 2 = 12

• x = 24
• x = 6
• x = 20
• x = 10

Multiple Choice

Solve the equation
3x = 27. 

• x = 24
• x = 81
• x = 9
• x = 3

Multiple Choice

10x = 90

• x = 80
• x = 100
• x = 10
• x = 9

Multiple Choice

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

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

Multiple Choice

17 = x + 3

• x = 20
• x = 14
• x = 13
• x = 19

Multiple Choice

Solve for x:

• x = 20
• x = 7
• x = 10
• x = 3

Multiple Choice

Solve the equation:
4p = 16

• p = 12
• p = -12
• p = -4
• p = 4

Multiple Choice

y/3=12

• 36
• -36
• 4
• -4

Multiple Choice

The first step to solving the equation g - 3 = -12 is to . . .

• divide by -3 on both sides of the equal sign

• multiply by -3 on both sides of the equal sign

• subtract 3 on both sides of the equal sign

• add 3 on both sides of the equal sign

Multiple Choice

From the last equation g - 3 = -12, after you add 3 on both sides of the equal sign, what is your answer?

• g = -15

• g = -9

• g = 36

• g = 15

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

What is the first step in solving for w in the equation 3w + 5 = 14?

• Add 5 to both sides of the equal sign

• Divide by 3 on both sides of the equal sign

• Subtract 5 from both sides of the equal sign

• Multiply by 3 on both sides of the equal sign

Multiple Choice

In the equation 5d - 1= 2d - 7, we need to get the variable to one side of the equal sign. What would we do to move the variable to the left side?

• -2 from both sides of the equal sign

• -5d from both sides of the equal sign

• -2d from both sides of the equal sign

• + 7 on both sides of the equal sign

Multiple Choice

In the equation 5d - 1= 2d - 7, after we -2d from both sides, we get 3d - 1 = -7. What does d = if you finish solving it?

• d = -1

• d = 1

• d = 2

• d = -2

Multiple Choice

A toy company spends $1500 per day for factory expenses plus $8 to make each teddy bear.  They sell the teddy bears for $12 a piece.  Which equation could be used to find the number of bears t the company has to sell in one day to equal its daily cost?

• 1500 + 8t = 12

• 12 + 8t = 1500

• 1500 + 8t = 12t

• 8t = 12t + 1500

Draw

Let's Now Do the Worksheet