2-Step and Multi-Step Equations

Multiple Choice

Solve 2x - 3 = 1 

• 3
• 2
• 1
• -2

Multiple Choice

Which operation would you use to solve this equation,  $$x+4=15$$  

• Add 4

• Subtract 4

Multiple Choice

Which operation would you use to solve this equation,  $$-3x=-24$$  

• Add 3

• Divide 3

• Divide -3

Multiple Choice

Which operation would you use to solve this equation,  $$\frac{x}{4}=3$$  

• Add 3

• Divide 3

• Divide -3

• Multiply 4

Multiple Select

What 2 operations are in this equation,  $$-3x+4=-24$$  

• Add

• Subtraction

• Multiply

• Divide

​Solving 2 Step Equation

​To solve a 2 step equation we are still going to do the inverse (opposite).

​1. First step is to do addition or subtraction

​2. Second step is to multiply or divide.

Multiple Choice

What operation will we do first,  $$-3x+4=-24$$  

• Add 4

• Subtract 4

• Multiply -3

• Divide -3

Multiple Choice

What operation will we do second,  $$-3x+4=-24$$  

• Add 4

• Subtract 4

• Multiply -3

• Divide -3

Multiple Choice

Solve  3x - 7 = 32

• 13
• -13
• 12
• -12

Multiple Choice

Solve    -3x + 5 = -16

• 9
• 8
• -7
• 7

Multiple Choice

Solve    2x -7 = -23

• -8
• 8
• -7

Multiple Choice

Solve     9 + 3x = 10

• 2/3
• 1/3
• -1/3
• 4

Multiple Choice

Solve    8 - 2x = 30

• -11
• 11
• -12
• 12

Multiple Choice

Solve    12 - 6y = 24

• -1
• -2
• -3
• -4

Multiple Choice

What is the first step (after setting up your workspace) in solving this equation:
5x + 7 = 12

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

Multiple Choice

3c + 5 = 23

• c = 3
• c = 6
• c = 7
• c = 18

Multiple Choice

4x + 7 = 23

• x = 16
• x = 4
• x = 9
• x = 12

Multiple Choice

Solve -2w + 10 = 56

• 23
• -23
• 33
• -33

Multiple Choice

Solve  7 - x = -5 

• x = 2
• x = -2
• x = 12
• x = -12

Multiple Choice

• t = 20
• t = -20
• t = -40
• t = 40

Multiple Choice

Is 5 a solution for 3x + 4 = 19

• yes
• no

Multiple Choice

Solve for k:
3k + 5 = 23

• k = 4
• k = 5
• k = 6
• k = 7

Multiple Choice

The steps in solving 5b - 6 = 24 are: 

• 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

WRITE AN EQUATION

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?

• 24-10=7x

• 7x- 24=10

• 7x+ 10=24

• 10+x=14

​

Simplifying before Solving

​

As you can see in the photo to the right, some equations must be simplified before they can be solved.​

​

The goal is to simplify the equation into a two-step equation.​

​The first 3 steps of this problem show how to simplify the equation.

After simplifying, we can see that ​we have a two-step equation and we use inverse operations to solve.

​

​

​

If an equation contains parentheses, like the ones you see in these examples, you must distribute the value on the outside to get rid of the parentheses.

​

Remember, distribute means to multiply!​

Distributive Property

​

​With all POSITIVE values.

​Be careful with negatives!

Multiple Choice

5(a + 6)

• 5a + 6

• a + 30

• 5a + 30

• 5a - 30

Multiple Choice

Which of the following is equivalent to 2(c - 8)?

• 2c - 16
• 2c + 16
• 2c - 8
• c - 16

Multiple Choice

When an equation has parentheses, which operation should we use to simplify and get rid of the parentheses?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

-9(g - 3)

• -9g + 27

• 9g + 27

• -9g + -27

• -9k - 27

​

Sometimes, to simplify an equation, it could involve combining like terms.

​

As you can see in the example, regrouping the like terms makes it easier to combine.​

​

Combine Like Terms

When combining like terms, pay attention to the sign in front of each term.

Combining could mean we add or subtract.​

Multiple Choice

Simplify the expression:

$$3a+7-2a$$  

• 8a

• 12a

• a + 7

• 5a + 7

Multiple Choice

Simplify the expression:

$$n-10+9n-3$$  

• -3
• 9n-3
• n
• 10n -13

Multiple Choice

Simplify the expression:

$$4x-3+2-2x$$  

• 6x + 5

• 2x + 1

• 2x - 1

• 6x - 1

Multiple Choice

Simplify the expression:

$$-9w+7-4w-16$$  

• -13w -9

• 5w -23

• -13w - 23

• -5w - 9

COPY THIS DOWN IN YOUR NOTES!!!
What are multi-step equations?
Check your neighbors to be sure they copy this!

• Equations that are solved using two or more steps

• Step 1: Distributive Property

• Step 2: Combine Like Terms

• Step 3: Solve the two-step equation.

Multiple Choice

Solve the following problem for x.

9x + 1 - 7x - 5 = - 20

• 1

• -13

• 4

• -7

Multiple Choice

Solve the following problem for x.

7x + 2 (x + 6) = 39

• 3

• 3.67

• 5

• 12

Multiple Choice

Solve the following problem for x.

4x - (7 - 6x) = 23

• -8

• 1.6

• 5

• 3

Multiple Choice

Solve the following problem for x.

-(3x - 9) + 10 = 70

• 11

• -18

• 23

• 3

Multiple Choice

7 + 3x + 4 =23

• x = 20/3
• x = 4
• x = 12
• x = 34/3

Multiple Choice

3x + 8x - 8 = 3

• 4

• 3

• 2

• 1

Multiple Choice

8v - 4v - 32 = 8

• 2

• 10

• 4

• -4

Fill in the Blanks

5 (y - 2) - 7y = -32

What is the first step?

Fill in the Blanks

5y - 10 - 7y = -32

What is the step is after distributing?

Fill in the Blanks

Solve: -10 - 2y = -32

Poll

Rate your current confidence when solving basic 1-2 step and Multi-step equations

• I feel very confident! I can help others.

• I usually get the answer right but I’m not very confident.

• I know the steps but I usually make a mistake along the way.

• I really don’t know what I’m doing.

• Photo math counts, right?!