Two step equations

Solving Two-Step Equations

​Quess the mystery number

Let's say I have a mystery number. If I multiply it by 2 and then add 5, I get 11. Guess what the number is?

Multiple Choice

What is the mystery number

• 11

• 2

• 3

• 5

Multiple Choice

Which of the following correctly represents the problem?

• 2x+5=11

• x+7=11

• 11−5=x

• 11−7=x

How do you solve for x?
You need to work your way backwards to get x by itself.

The last step was to add 5, so we need to undo that first.  How do we undo adding 5? We need to use the inverse operation and subtract 5 from both sides.  

Now that we've canceled out the addition, we're left with the equation 2x = 6.  
The 2 in front of the x means that x is being multiplied by 2.

 To get x by itself, we need to undo this multiplication.

Multiple Select

How do you solve for x? (select all that apply)

• Perform opposite operation

• inverse operation

• work backwards

• add/suntract then

  multiply/divide

Multiple Choice

How do we undo multiplication?

• ADD

• Subtract

• Multiply

• Divide

​How do we undo this multiplication?

We need to divide

Therefore, we can can cancel out the 2 by dividing both sides by 2.

Always remember:

Whatever you do to one side of the equation, you must do to the other to keep it balanced

Plug 3 in for x in the original equation and make sure the left side simplifies to 11.
Original Equation: 2x+5=11

Step 1: Replace x with 3: 2(3)+5=11
Step 2: Simplify : 6+5=11
Both sides of the equation are equal, so answer x=3 is correct

After solving for x, it’s important to check your answer to ensure it's correct.

Check Your Work:

When you're solving an equation, the goal is to get the variable by itself.  We need to work our way backwards to figure out what x was. 

So given the equation

remember:Undo the addition/subtraction first
therefore, we're left with x/4 = 5.  This means that x is being divided by 4.  

We need to use the inverse operation and multiply.

Now, we will multiply both sides by 4 to cancel the division by 4.  

Multiple Choice

What is the first step in solving this equation:
5x + 7 = 12

• Divide by 5

• Add 7

• Subtract 7

• 
  multiply by 5

Multiple Choice

What is the first step in solving the following equation?
3x - 5 = 20

• multiply both sides by 5
• add 5 to both sides
• divide both sides by 5
• subtract both sides by 5

Multiple Choice

Solve: $$7\ +\ \frac{a}{3}=\ 5$$  

• a= -2

• a= -6

• a= 3

• a= 15

Multiple Choice

Which step should you perform first in the following equation:

$$21\ =\ 9\ -\ 4g$$  

• Divide both sides by -4

• Divide both sides by 4

• Add 9 to both sides

• Subtract 9 from both sides

Multiple Choice

Which step should you perform second in the following equation:

$$21\ =\ 9\ -\ 4g$$  

• Divide both sides by -4

• Divide both sides by 4

• Add 9 to both sides

• Subtract 9 from both sides

Multiple Choice

What is the first step to solve for x. $$-9\ +\ 3x\ =\ 10$$  

• Subtract 9 from both sides of the equation.

• Add 9 to both sides of the equation.  

• Subtract 3 from both sides of the equation.

• Add 10 to both sides of the equation.  

Multiple Choice

Solve: $$\frac{x}{7}+2=5$$  

• $$x=1$$  

• $$x=49$$  

• $$x=7$$  

• $$x=21$$  

Multiple Choice

Solve: 4y + 1 = 13

• 4
• 7
• 3
• 2

Multiple Choice

Solve for x. $$\frac{x}{7}-8=16$$  

• x = 56

• x = 8/7

• x = 24/7

• x = 168

Multiple Choice

Solve: 9 = 2s + 1 

• 4
• -4
• 3.5
• 5

Multiple Choice

What is the first step to solve this equation:
11 - 3x = 44

• Add 3 to both sides
• Subtract 11 from both sides
• Add 11 to both sides
• Divide 3 on both sides.

Multiple Choice

Identify the steps to solve for b

• Add 6 to both sides and divide both sides by 5

• Add 6 to both sides and multiply both sides by 5

• Subtract 6 from both sides then multiply both sides by 5

• Subtract 6 from both sides then divide both sides by 5

Multiple Choice

Solve: 4x + 22 = -34

• -14
• -22
• 16
• -20

Multiple Choice

What is the first step in solving this equation:
5x + 7 = 12

• Divide by 5
• Subtract 5
• Multiply by 7
• Subtract 7

Multiple Choice

Solve: 8 + 3h = 26

• h = 6
• h = 7
• h = 8
• h = 9

Multiple Choice

Solve: 13= 5m -2

• -3

• 2

• 3

• -2

Multiple Choice

Solve: 9=4g+13

• 1

• -1

• 0

• 3

Multiple Choice

Solve:  $$\frac{x}{3}+5=-1$$  

• -2

• -18

• 18

• 12

Multiple Choice

Solve:  $$\frac{x}{4}+11=20$$  

• 9

• 36

• 9/4

• 31/4