One Step Equations Study Guide

One Step Equations Study Guide

​Students will review the following concepts.

• Properties of Equality

• Inverse Operations

• Solving & Writing

  • Addition Equations

  • Subtraction Equations

  • Multiplication Equations

  • Division Equations

• Substitution Method ( to check equations)

• Decode Word Problems

Solving Equations Strategies

• Use inverse operation to isolate the variable (get the variable alone).

• Keep the equation balanced by performing the operation on both sides of the equal sign, using one of the four properties of equality.

  • When solving an equation, you may have to remove a number from one side of the equation in order to isolate the variable.

    • Addition Property of Equality

    • Subtraction Property of Equality

    • Multiplication Property of Equality---------------->

    • Division Property of Equality

Addition Property of Equality

• Add the same value to the left side and right side of the equal sign to keep the equation balanced.

Subtraction Property of Equality

• Subtract the same value to the left side and right side of the equal sign to keep the equation balanced.

Multiplication Property of Equality

• Multiply the same value to the left side and right side of the equal sign to keep the equation balanced.

Division Property of Equality

• Divide the same value to the left side and right side of the equal sign to keep the equation balanced.

Inverse means the opposite. So in math, an inverse operation can be defined as the operation that undoes what was done by the previous operation.

For example:

The inverse of + 3 is – 3

Solve y +14=20

• The inverse operation of addition is subtraction.

• Subtract 14 from both sides of the equal sign

• 20-14=6

• y=6

Solve x -120 = 80

• The inverse operation of subtraction is addition

• Add 120 to both sides of the equal sign.

• 80 +120= 200

• x=200

Solve 3n=12

• The inverse operation of multiplication is division

• Divide both sides by 3

• 12/3=4

• n=4

• The inverse operation of division  is multiplication 

• Multiply both sides by 2

• 16(2)=32

• k=32

As you practice skills where calculations are necessary, use your whiteboard. No calculators are allowed during this task.

​

Let's Practice!!!

Multiple Choice

What is the inverse operation of Multiplication?

• addition

• subtraction

• multiplication

• division

Multiple Choice

What is the inverse operation of addition?

• addition

• subtraction

• multiplication

• division

Multiple Choice

What is the inverse operation of subtraction?

• addition

• subtraction

• multiplication

• division

Multiple Choice

What is the inverse operation of Division?

• addition

• subtraction

• multiplication

• division

Multiple Choice

The main goal of solving equations is to get the _________ by itself.

• Coefficient

• Variable

• Constant

• Term

Multiple Choice

Using the "opposite operation" to "undo" and isolate the variable when solving an equation is more commonly called...

• Inverse operations

• math

• variable

• PEMDAS

Multiple Choice

Solve the equation using the inverse operation and property of equality.

12 = 4a

• 48

• 3

• 8

Multiple Choice

Solve the equation using the inverse operation and property of equality.

x + 12 = 20

• x = 32

• x = -32

• x = 8

• x = -8

Multiple Choice

Solve the equation using the inverse operation and property of equality.

• x = 20

• x = 7

• x = 10

• x = 3

Multiple Choice

Solve the equation using the inverse operation and property of equality.

3x = 27. 

• x = 24

• x = 81

• x = 9

Multiple Choice

Solve the equation using the inverse operation and property of equality.

x - 32 = 49

• x = 17

• x = 71

• x = 81

• x = 49

Multiple Choice

Solve the equation using the inverse operation and property of equality. $$12\ =\ \frac{a}{4}$$  

• 48

• 3

• 8

Multiple Choice

Solve the equation using the inverse operation and property of equality.

c - 5 = 8

• 3

• 13

• 5

• 8

Multiple Choice

Solve the equation using the inverse operation and property of equality. $$21\ =\ 14\ +\ x$$  

• x = 7

• x = 35

• x = 294

• x = 1.5

Multiple Choice

Solve the equation using the inverse operation and property of equality. $$\frac{m}{5}\ =\ 10$$  

• 2

• 5

• 50

Multiple Choice

Solve the equation using the inverse operation and property of equality.

m + 4 = 12

• 16

• 8

• 48

• 3

Multiple Choice

Complete the sentence.

When solving an equation, our goal is to____________.

• add all the numbers together.

• use a calculator.

• eat lunch.

• isolate the variable to solve.

Multiple Choice

Why do you add 7 to both sides?

• To undo addition, you subtract.

• To balance the equation, you subtract 7 on both sides.

• To undo subtraction, you add.

• To balance the equation,you add 7 to both sides.

Multiple Choice

What property of equality is shown below?

25 + d = 36

25 + d - 25 = 36 - 25

• addition property of equality

• subtraction property of equality

• division property of equality

• multiplication property of equality

Multiple Choice

What property of equality is shown below?

y - 12 = 30

y -12 + 12 = 30 +12

• addition property of equality

• subtraction property of equality

• multiplication property of equality

• division property of equality

Multiple Choice

Which property justifies the work in solving this equation?

• Addition Property of Equality

• Multiplication Property of Equality

• Commutative Property of Addition

• Subtraction Property of Equality

Multiple Choice

What property of equality is shown below? 7n=28 7n $$\div$$  7 = 28  $$\div$$  7

• addition property of equality

• subtraction property of equality

• multiplication property of equality

• division property of equality

Multiple Choice

Identify the property you would use to solve this equation:
4x = 72

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Multiple Choice

Identify the property you would use to solve this equation:
y – 7 = 28

• Additive Property of Equality

• Subtraction Property of Equality

• Multiplicative Property of Equality

• Division Property of Equality

Multiple Choice

What property would I use to solve this equation?
7 + x = 14

• Multiplication Property

• Subtraction Property

• Division Property

• Substitution Property

Multiple Choice

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

• add 5 to both sides

• add 15 to both sides

• subtract 15 from both sides

• subtract 5 from both sides

Multiple Choice

Solve the equation using the inverse operation and property of equality.

x + 4 = -3

• x = -1

• x = 4

• x = -7

• x = 8

The next slides will help you practice word problems. Be sure to review words that mean certain operations.

Write & Solve Equations from Word Problems

​Equation Phrases

Expression Phrases

Multiple Choice

Ava bought stickers to give 12 of her friends. Each friend received 4 stickers. How many stickers did she bring to school? Which equation best represents this situation?

• $$\frac{\times}{12}=4$$

• 12x = 4

• 4x =12

• $$\frac{12}{\times}=4$$

Multiple Choice

Which property of equality would you use to solve the equation 14x = 56?

• Addition Property of Equality

• Subtraction Property of Equality

• Division Property of Equality

• Multiplication Property of Equality

Multiple Choice

Which of the following can always be used to check your solution to your equation?

• distributive property
• difference
• substitution
• mean

Multiple Choice

Choose the correct equation for the situation.
Jane is 3 years older than Sam. If Jane 12, how old is Sam?

• j - 3 = 12

• s - 3 = 12

• s + 3 = 12

• j + 12 = 3

Multiple Choice

Sally bought three candy bars for a total of $18.00. How much did each candy bar cost? Write an equation to solve this problem. Use c as your variable.

• 18c=6

• c + 6= 18

• c +18 = 6

• 3c=18

Multiple Choice

Gabe is saving an equal amount each week for 4 weeks to buy a $60 video game.  Write an equation to determine how much he needs to save each week. 

• m + 4 = 60
• 4m = 60
• 60 - m = 4
• m/60 = 4

Multiple Choice

Amy was given an amount of money, m, for a good grades on her report card. She spent $15.00 and now has $25.32. How much money did she get for good grades? Write an equation you could use to solve this problem. Use m as your variable.

• m - 25.32 = 15

• m/25.32 = 15

• m - 15 = 25.32

• 15m = 25.32

Multiple Choice

WRITE AN EQUATION

At a restaurant, Mike and his three friends decided to divide the bill evenly. If each person paid $13 then what was the total bill?

• 4x = 13

• x/3 = 13

• 13(4) = x

• x/4 = 13

Multiple Choice

Ava bought stickers to give 12 of her friends. Each friend received 4 stickers. How many stickers did she bring to school? Which equation best represents this situation?

• $$\frac{\times}{12}=4$$

• 12x = 4

• 4x =12

• $$\frac{12}{\times}=4$$

Multiple Choice

2. Cheryl gets paid $8 per hour for her job at the record store.  She made a total of $96 last week.  Which equation models this situation?

• 96h = 8
• h/96 = 8
• 8h = 96
• h/8 = 96

Multiple Choice

What is the inverse operation of division?

• Division
• Multiplication
• Addition
• Subtraction

Multiple Choice

Ken is thinking of a number. Nine more than the product of 4 and the number is 73. What is the equation?

• 4 + 9x = 73
• 4x = 73
• 4x + 9 = 73
• 9x + 4 = 73

Multiple Choice

Reagan earned $5.00 for allowance. She bought an ice cream cone for $1.25 and a pack of stickers for 50 cents. How much money does Mandy have left?

• 3.25
• 6.75
• 4.35
• 11.75

Multiple Choice

Colleen recently learned how to knit and wants to make a scarf for her aunt. She wants the scarf to be s inches long. She started knitting and has completed 18 inches so far. Colleen has 42 inches left to knit.

Which equation models the story?

• $$s\ +\ 18\ =\ 42$$

• $$18s\ =\ 42$$

• $$\frac{s}{18}=42$$

• $$s\ -\ 18\ =\ 42$$

Multiple Choice

Alice signed up to bake chocolate chip and oatmeal raisin cookies for a bake sale. After she made c chocolate chip cookies, Alice decided to make 12 fewer oatmeal raisin cookies, since they are less popular. She only made 24 oatmeal raisin cookies.

Which equation models the story?

• $$c\ +\ 12\ =\ 24$$

• $$c\ -\ 12\ =\ 24$$

Multiple Choice

Zoe sells handmade jewelry at craft fairs. She bought a package of c charms. She used all the charms in the package to make 12 bracelets, and each bracelet had 8 charms.

Which equation models the story?

• $$8c\ =\ 12$$

• $$\frac{c}{12}\ =\ 8$$

Multiple Choice

Ms. Carter bought m miniature candy bars for a class party. She plans to split the candy bars evenly among 8 prize bags for a game they will play. She will put 4 candy bars in each prize bag. 

Which equation models the story?

• $$4m\ =\ 8$$
  

• $$\frac{m}{8}=\ 4$$

Multiple Choice

At soccer practice, Levi's team spent m minutes practicing drills. They wanted to practice 3 different drills. So, they spent 6 minutes on each.

Which equation models the story?

• $$\frac{m}{3}=\ 6$$

• $$3m\ =\ 6$$

Take a moment to answer questions based on how you feel about each concept. Be sure to practice IXL where you need more practice.

How do you feel about the concepts?

Poll

How well do you understand inverse operations?

• Not Well At All!

• Fairly Well!

• Getting Better!

• Very Well!

Poll

How well do you understand properties of equality?

• Not Well At All!

• Fairly Well!

• Getting Better!

• Very Well!

Poll

How well do you understand solving addition equations using inverse operations and property of equality strategy?

• Not Well At All!

• Fairly Well!

• Getting Better!

• Very Well!

Poll

How well do you understand solving subtraction equations using inverse operations and property of equality strategy?

• Not Well At All!

• Fairly Well!

• Getting Better!

• Very Well!

Poll

How well do you understand solving multiplication equations using inverse operations and property of equality strategy?

• Not Well At All!

• Fairly Well!

• Getting Better!

• Very Well!

Poll

How well do you understand solving division equations using inverse operations and property of equality strategy?

• Not Well At All!

• Fairly Well!

• Getting Better!

• Very Well!

Poll

How well do you understand writing equations from a word problem or phrase?

• Not Well At All!

• Fairly Well!

• Getting Better!

• Very Well!

Poll

Are you quiz ready???

How prepared do you feel for tomorrow's quiz?

• I'm soooo not quiz ready!

• I am ready for solving addition and subtraction equations, but not multiplication or division equations.

• I am ready for most of the concepts from this lesson, I just need to practice more.

• I understand all of the concepts! I am quiz ready! Let's go!