One and Two Step Equations

One and Two Step Equations

Solving Algebraic Equations

Throughout this unit, we will focus on how to solve algebraic equations for a given variable.

The way we solve an equation in algebra is we work through BEDMAS backwards to undo everything and get our variable by itself. We need to perform the opposite operation.

BEDMAS stands for:
B = brackets
E = exponents
D = division
M = multiplication
A = addition
S = subtraction

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​Reminder:

When we solve an algebraic equation, think of it like a scale. Whatever we do on one side, we have to do it on the other side.

So, for example, if I remove 1 apple on one side, I have to remove 1 apple on the other side so it stays balanced

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Scale

In order to solve a one-step equation, we need to "undo" anything on the side with the x.

​One-Step Equation

In this case, there is a +20 on the x side, so we undo it by subtracting 20.

But remember, whatever we do on one side, we also have to do it on the other side!

​One-Step Equation

x + 20 = 45

Subtract 20 on both sides.

We're left with:

x = 25.

​One-Step Equation

It might have been obvious from the start that x has to be 25
(because 25 + 20 = 45),
but it's still important to understand the steps for more complex equations.

​One-Step Equation

Example 2

3x = 15

Remember, 3x means 3 times x.
The opposite of times is divide, so we need to divide by 3 on both sides.

We get x = 5

You Try!

Try to solve these one-step equations! Remember: Perform the opposite operation!

Multiple Choice

What is the inverse operation of subtraction?

• Subtraction
• Multiplication
• Division
• Addition

Multiple Choice

What is the inverse operation of division?

• Division
• Multiplication
• Addition
• Subtraction

Multiple Choice

In the equation
x + 7 = 12
7 is being added to the variable, x. How should you show your work to isolate the variable and solve the equation? 

• Subtract 7 from both sides. The solution is x = 5.
• Add 7 to both sides.
  The solution is x = 19.
• Multiply both sides by 7 The solution is x = 84.

Multiple Choice

5n = 30

• n = 8

• n = 12

• n = 6

• n = 5

Multiple Choice

n - 4 = -12

• n = 12

• n = 10

• n = -8

• n = -16

Multiple Choice

x + 13 = 25

• x = 15

• x = 12

• x = 10

• x = 11

Multiple Choice

x + 8 = 15

• x = 7

• x = 8

• x = 9

• x = 6

Multiple Choice

-6y = 42

• y = -6

• y = -7

• y = -42

• y = -12

Multiple Choice

$$\frac{n}{2}$$ = 5

• n = 10

• n = 2

• n = 5

• n = 20

Multiple Choice

$$\frac{x}{-4}=10$$

• x = -40

• x = -4

• x = 16

• x = 36

Two-Step Equations

Two-step equations require 2 steps to solve them.

The 2 steps (usually) are:
1. Get rid of the extra number on the x side by doing the opposite
2. Multiplying or dividing the number that's with the x to get x by itself.

We divide both sides by 2, and we're left with:

x = 4

So the solution is x = 4.

Step 2: Get rid of the 2

We subtract 5 on both sides of the equal sign, and we're left with:
2x = 8

Step 1: Get rid of the 5

Example: 2x + 5 = 13

Divide both sides by -3, we get:
x = -7

So the solution is x = -7.

Step 2: Get rid of the -3

Add 7 on both sides to get:

-3x = 21

Step 1: Get rid of the -7

Example 2: -3x - 7 = 14

Multiply both sides by 3 to get:
x = 30

So the solution is x = 30.

Step 2: Get rid of the 3

Step 1: Get rid of the +2

You Try!

Try to solve these two-step equations! Remember: Perform the opposite operations!

Multiple Choice

Solve for x: 4x+1 = 9

• x = 1

• x = 2

• x = 3

• x = 4

Multiple Choice

Solve for x: 3x+2 = 11

• x = 1

• x = 2

• x = 5

• x = 3

Multiple Choice

Solve for x: 5x+3 = 53

• x = 5

• x = 10

• x = 12

• x = 14

Multiple Choice

Solve for x: 3x-1 = 11

• x = 1

• x = 5

• x = 4

• x = 2

Multiple Choice

Solve for x: 4x-1 = 39

• x = 39

• x = 20

• x = 12

• x = 10

Multiple Choice

Solve for x: $$\frac{x}{2}-1=10$$

• x = 2

• x = 5

• x = 9

• x = 22

Multiple Choice

Solve for x: $$\frac{x}{3}-2\ =\ 1$$

• x = 3

• x = 9

• x = 12

• x = 5

Multiple Choice

Solve for x: $$\frac{x}{5}-1=4$$

• x = 5

• x = 25

• x = 4

• x = 12

Multiple Choice

Solve for x: $$\frac{x}{7}-4=0$$

• x = 14

• x = 24

• x = 28

• x = 7

Multiple Choice

$$\frac{x}{5}+3=9$$

• x = 35

• x = 25

• x = 30

• x = 20

Next Lesson

In our next lesson, we will look at more complex algebraic equations, including how to solve equations that have x terms on both sides of the equation.