Solving Multi-step Equations including steps on how to solve.

Question 1

Define multi-step equation.

Answer 1

An equation that requires more than one operation to solve for the variable.

Question 2

What is the first step in solving a multi-step equation?

Answer 2

Combine like terms on both sides of the equation.

Question 3

True or false: You can add or subtract from both sides of an equation.

Answer 3

TRUE

This maintains the equality of the equation.

Question 4

Fill in the blank: To isolate the variable, you should first _______ the constant term.

Answer 4

move

Question 5

What does it mean to isolate a variable?

Answer 5

To get the variable alone on one side of the equation.

Question 6

Define like terms.

Answer 6

Terms that have the same variable raised to the same power.

Question 7

What is the purpose of distributing in an equation?

Answer 7

To eliminate parentheses by multiplying the term outside by each term inside.

Question 8

True or false: You can multiply or divide both sides of an equation by zero.

Answer 8

FALSE

This would make the equation undefined.

Question 9

Fill in the blank: When solving for x, always check your _______.

Answer 9

solution

Question 10

What is the inverse operation of addition?

Answer 10

Subtraction

Question 11

What is the inverse operation of multiplication?

Answer 11

Division

Question 12

True or false: You can change the order of operations in an equation.

Answer 12

FALSE

The order of operations must be followed.

Question 13

Define coefficient.

Answer 13

A numerical factor in a term of an algebraic expression.

Question 14

What is the first step when you see parentheses in an equation?

Answer 14

Use the distributive property to eliminate the parentheses.

Question 15

Fill in the blank: To solve 3x + 5 = 20, first _______ 5 from both sides.

Answer 15

subtract

Question 16

What do you do after isolating the variable term?

Answer 16

Divide or multiply to solve for the variable.

Question 17

True or false: You can add a term to one side without affecting the other side.

Answer 17

TRUE

This keeps the equation balanced.

Question 18

Define equation.

Answer 18

A mathematical statement that asserts the equality of two expressions.

Question 19

What is the goal when solving an equation?

Answer 19

To find the value of the variable that makes the equation true.

Question 20

Fill in the blank: The solution to an equation is the value of the _______.

Answer 20

variable

Question 21

What is the first operation to perform in the equation 2(x + 3) = 14?

Answer 21

Distribute the 2 to both terms inside the parentheses.

Question 22

True or false: You can simplify both sides of an equation independently.

Answer 22

TRUE

This helps in reducing the complexity of the equation.

Question 23

Define constant term.

Answer 23

A term in an equation that does not contain any variables.

Question 24

What should you do if you have fractions in an equation?

Answer 24

Multiply through by the least common denominator to eliminate them.

Question 25

Fill in the blank: The equation 4x - 8 = 0 can be solved by first _______ 8.

Answer 25

adding

Question 26

What is the **final step** in solving a multi-step equation?

Answer 26

Check your solution by substituting it back into the original equation.

Question 27

True or false: The solution to an equation can be a fraction.

Answer 27

TRUE ## Footnote Solutions can be any real number, including fractions.

Question 28

Define **solution set**.

Answer 28

The set of all possible solutions to an equation.

Question 29

What do you do after combining like terms?

Answer 29

Perform inverse operations to isolate the variable.

Question 30

Fill in the blank: In the equation 5x + 10 = 35, you first _______ 10.

Answer 30

subtract

Question 31

What does it mean to **check your work**?

Answer 31

To substitute your solution back into the original equation.

Question 32

True or false: An equation can have no solution.

Answer 32

TRUE ## Footnote This occurs when the variable cancels out and results in a false statement.

Question 33

Define **variable**.

Answer 33

A symbol used to represent an unknown value in an equation.

Question 34

What is the **first step** in solving 3(x - 2) = 12?

Answer 34

Distribute the 3 to both terms inside the parentheses.

Question 35

Fill in the blank: To solve for x in 2x + 4 = 12, first _______ 4.

Answer 35

subtract

Question 36

What is the **next step** after isolating the variable term?

Answer 36

Divide by the coefficient of the variable.

Question 37

True or false: You can rearrange an equation in any order.

Answer 37

TRUE ## Footnote As long as you maintain equality, you can rearrange terms.

Question 38

Define **algebraic expression**.

Answer 38

A combination of numbers, variables, and operations without an equality sign.

Question 39

What is the **distributive property**?

Answer 39

A property that states a(b + c) = ab + ac.

Question 40

Fill in the blank: In the equation 7x = 21, to find x, you must _______ by 7.

Answer 40

divide

Question 41

What do you do if both sides of an equation are equal?

Answer 41

The equation is true for any value of the variable.

Question 42

True or false: You can solve equations with variables on both sides.

Answer 42

TRUE ## Footnote You can move variables to one side to simplify.

Question 43

Define **linear equation**.

Answer 43

An equation that forms a straight line when graphed.

Question 44

What is the **goal** of solving multi-step equations?

Answer 44

To find the value of the variable that satisfies the equation.

Question 45

Fill in the blank: The term **constant** refers to a value that _______.

Answer 45

does not change

Question 46

What is the **key** to solving multi-step equations?

Answer 46

Performing operations systematically to isolate the variable.

Question 47

True or false: The solution to an equation can be negative.

Answer 47

TRUE ## Footnote Solutions can be any real number, including negatives.

Question 48

Define **equivalent equations**.

Answer 48

Equations that have the same solution set.