Solving One-Step Equations

Solving One-Step Equations

Learning Objective- I can solve one-step equations that have one variable.

Lesson Vocabulary

-Equivalent equations

-Addition Property of Equality

-Subtraction Property of Equality

-Isolate

-Inverse Operations

-Multiplication Property of Equality

-Division Property of Equality

Equivalent Equations-

Equations that have the same solution(s). You can apply the same operation to each side of an equation to get an equivalent equation.

Addition Property of Equality-

Adding the same number to each side of an equation produces an equivalent equation.

Ex.

 $x-3=2$  

Add 3 to both sides 
 $x-3\left(+3\right)=2\left(+3\right)$  
-3+3=0   2+3=5
Therefore:
x=5

Subtraction Property of Equality-

Subtracting the same number from each side of an equation produces an equivalent equation.

Ex.

  $x+3=2$  

Subtract 3 from both sides
 $x+3\left(-3\right)=2\left(-3\right)$  
3-3=0     2-3=-1
Therefore:
x=-1

Isolate-

To solve an equation, you must isolate the variable. You do this by getting the variable alone on one side of the equation.

Inverse Operation-

An inverse operation undoes another operation. Fore example, subtraction is the inverse of addition.

Multiplication Property of Equality-

Multiplying each side of an equation by the same nonzero number produces an equivalent equation.

Ex.  $\frac{x}{3}=2$  

Multiply both sides by 3

 $\frac{x}{3}\left(\times3\right)=2\left(\times3\right)$  
x=6

Division Property of Equality-

Dividing each side of an equation by the same nonzero number produces an equivalent equation.
EX.  $5x=20$  

Divide both sides of the equal sign by 5
 $\frac{5x}{5}=\frac{20}{5}$  
x=4

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

Which equation has x = 5 as the solution?

• x + 15 = 10

• 2x = 5

• 2x = 10

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

x ÷ 2 = 12

• x = 24
• x = 6
• x = 20
• x = 10

Multiple Choice

Solve for x:

• x = 20

• x = 7

• x = 10

• x = 3

Multiple Choice

Solve the equation

3x = 27.

• x = 24

• x = 81

• x = 9

• x = 3

Multiple Choice

5. 6b = 30

• x = 36

• x = 24

• x = 180

• x = 5

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

x - 32 = 49

• x = 17
• x = 71
• x = 81
• x = 49

Multiple Choice

4 + b = 30

• -34

• 34

• -26

• 26

Multiple Choice

x + 12 = 20

• x = 32
• x = -32
• x = 8
• x = -8

Multiple Choice

17 = x + 3

• x = 20
• x = 14
• x = 13
• x = 19