Solving One- and Two-Step Equations

Solving One- and Two-Step Equations

A Quick Review

Linear Equations

• An equation that contains one variable

• Used to solve for an unknown value that makes the equation true.

Solutions to Linear Equations

• When you solve a linear equation, you are trying to find the unknown value (represented by the variable).

• You must keep both sides of the equation balanced by performing equal operations to both sides of the equal sign.

Solving Linear Equations

• To solve an equation, you must undo the equation by using inverse operations.

• The order of the operations you perform is important.

Multiple Choice

Which operation would you use to undo the following equation to solve for x?

x + 5 = 8

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

Which operation would you use to undo the equation and solve for x?

5x = - 20

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

Which operation would you use to undo the equation and solve for x?

 $\frac{x}{-6}=3$  

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

Which operation would you use to undo the equation and solve for x?

x - 9 = -10

• Addition

• Subtraction

• Multiplication

• Division

Solving Two-Step Equations

• These equations are called "two-step" because the equation involves more than one operation.

• The equation must be solved by undoing the order of the operations.

Inverse Order of Operations

To solve an equation with more than one operation, remember to work PEMDAS backwards!

Multiple Select

What two operations are shown in the equation  $8b+5=29?$   

• Addition

• Subtraction

• Multiplication

• Division

Inverse PEMDAS

• This equation contains multiplication (8b) and addition.

• To solve this equation, we undo the equation by working PEMDAS backwards and doing inverse operations.

• REMEMBER, when you solve an equation, anything you do to one side, you must do to the other side. It must stay balanced

Multiple Choice

Which operation would you perform first to undo the equation  $-3x+10=28$  ?

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

Which operation would you perform SECOND when trying to solve the equation  $-3x+10=28$  ?

• Addition

• Subtration

• Multiplication

• Division

Multiple Choice

Solve the equation:  $-4x+1=21$  

• x= 120

• x= 5

• x= 30

• x= -5

Multiple Choice

Solve the equation:  $3c+5=23$  

• c = 3

• c = 6

• c = 7

• c = 18

Multiple Choice

Solve the equation:  $5x+4=-6$  

• x= 2

• x= -2

• x= 10

• x= 15

Equations with Distributive Property

• If you see a set of parentheses in an equation, you will most likely need to simplify the expression by using the distributive property

• Distribute to remove the parentheses and then solve using inverse operation

Multiple Choice

Solve the equation: 4 = 2(x + 3)

• 
  

  $\frac{1}{2}$ =x
  

• $\frac{7}{2}$ = x

• -1 = x

• 5 = x