Multistep equations Mastery review

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

What is the first step in solving this equation?

• subtract 3 to both sides

• subtract the 6 - 2

• distribute 2

• distribute -2

Multiple Choice

What will the equation look like after you combine like terms?

• -5x + 5 = 35

• x + 5 = 35

• 5x + 5 = 35

• -x + 5 = 35

Multiple Choice

What is the first step in solving this equation?

• add 4 to both sides

• distribute the 4

• subtract 4 to both sides

• subtract 12 to both sides

Multiple Choice

What will the equation look like after you distribute?

• -6x - 8 = 10

• -6x + 8 = 10

• -5x - 6 = 10

• -5x + 6 = 10

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​Solving Multi-Step Equations

Follow along and answer the question in this Quizizz Lesson.

In case you need a little help, I have included some informational slides to help out.

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Simplifying before Solving

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

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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.

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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.

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Remember, distribute means to multiply!​

Distributive Property

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​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

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

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

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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

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Solving Multi-Step Equations

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​

​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.

​On the next few slides, you will be asked to simplify and solve a few equations. Please complete these examples on page 22 of your notebook.

Multiple Choice

Simplify the following equation and solve for x:

$$2x-3+4x=27$$  

• x = 12

• x = 4

• x = 5

• x = 15

Multiple Choice

Simplify the equation and solve for the variable.

$$24\ =\ 3\left(3x\ -7\right)$$

• $$x\ =\ -9$$  

• $$x\ =\ 5$$  

• $$x\ =3$$  

• $$x\ =\ 7$$  

Multiple Choice

Simplify the following equation and solve for x:

$$3x+2(4x-4)=3$$  

• x = 4

• x = 3

• x = 2

• x = 1

Multiple Choice

The objective when solving an equation is to....

• isolate the variable.

• check the solution.

• guess and check.

• Combine Like Terms.

Multiple Choice

Solve for v.

Hint for first step: What is the inverse of dividing by 3?

• 33

• -3

• 15

• -6.3

Fill in the Blank

$$4\left(3-v\right)-10=18$$  

v=?

Fill in the Blank

$$-3\left(-w+2\right)=-5w+2$$  

w=?

Fill in the Blank

$$4y+3-2y=-10+3y$$  

y=?

Multiple Choice

x + 7 = x + 6

• No solution

• Infinitely Many Solutions

• One solution of x = 1

• Two solutions of x = 1 or -1

Multiple Choice

Solve:

6(y + 4) = 6y + 10

• y = 10

• y = 24

• infinitely many solutions

• no solutions

Multiple Choice

What does it mean when an equation has infinitely many solutions?

• "To infinity and beyond"

• the equation is always TRUE when any value is substituted in for the variable

• the equation will NEVER be true when any value is substituted in for the variable

• only ONE solution will make the equation true

Multiple Choice

Solve:

10x + 3 + 3x = 5x + 1 + 8x + 2

• x = -3

• x = 3

• infinitely many solutions

• no solutions

Multiple Choice

$$\frac{1}{2}x-2\ =\ 3$$  

What is the value of x in this equation? 

• x = -2

• x = 5

• x = 3

• x = 10

Multiple Choice

$$-\frac{b}{2}-5\ =\ 1$$  

What is the value of b?

• b = 12

• b = -12

• b = 6

• b = -6

Multiple Choice

$$\frac{a}{4}-1\ =\ 5$$  

What is the value of a?

• a = 1/4

• a = 6/4

• a = 16

• a = 24

Multiple Choice

Solve:
$$3x-x+4=4\left(2x+1\right)$$  

USE PAPER TO DO YOUR WORK!!

• No Solution

• All Real Numbers 

• x = 6

• x = 0

Multiple Choice

What is the Second 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

What is the first step in the equation:

2x - 3 + 4x = 27

• Combine Like Terms

• Add 3 on both sides

• Divide by 2 on both sides

• Subtract 4x from both sides

Multiple Choice

What is the second step to solve the equation:

2x - 3 + 4x = 27

• Divide everything by 2

• Add 3 to both sides

• Divide everything by 6

• Subtract 3 to both sides

Multiple Choice

What is the last step to solve the equation:

2x - 3 + 4x = 27

• Add 4 on both sides

• Subtract 6 from both sides

• Subtract 27 from both sides

• Divide by 6 on both sides

Fill in the Blank

After Steps 1-3, what is the answer to:

2x - 3 + 4x = 27

Fill in the Blank

Solve for n:

4n - 1 = 6n + 8 - 8n + 15

Multiple Choice

Where did Rajendra make an error in his calculation?

• Step 1

• Step 2

• Step 3

• Rajendra is correct.

Multiple Choice

Is there a mistake on the equation solved? If so where was the mistake made?

• This equation is solved correctly.

• The mistake was made on the first step of combining like terms on the left side.

• The mistake was made on the second step of moving the variable to the left side.

• The mistake was made on the third step of moving the constant to the right side.

• The mistake was made on the last step when isolating the variable by removing the coefficient

Multiple Choice

Is there a mistake on the equation solved? If so where was the mistake made?

• This equation is solved correctly.

• The mistake was made on the second step of combining like terms on the left side.

• The mistake was made on the third step of moving the variable to the right side.

• The mistake was made on the fourth step of moving the constant to the left side.

• The mistake was made on the first step doing the distributive property.

Multiple Choice

Is there a mistake on the equation solved? If so where was the mistake made?

• This equation is solved correctly.

• The mistake was made on the second step doing the distributive property on the right side.

• The mistake was made on the third step of moving the variables.

• The mistake was made on the fourth step of determining true/false statement as infinite vs no solution.

• The mistake was made on the first step doing the distributive property on the left side.

Multiple Choice

Is there a mistake on the equation solved? If so where was the mistake made?

• This equation is solved correctly.

• The mistake was made on the first step of doing the distributive property.

• The mistake was made on the second step of moving the variable.

Multiple Choice

Is there a mistake on the equation solved? If so where was the mistake made?

• This equation is solved correctly.

• The mistake was made on the distributive property step on the right side.

• The mistake was made on combining like terms on the left side.

• The mistake was made on moving the variable to the left side.

• The mistake was made on moving the constant to the right side.

Multiple Choice

Is there a mistake on the equation solved? If so where was the mistake made?

• This equation is solved correctly.

• The mistake was made on the distributive property step.

• The mistake was made on combining like terms on either side.

• The mistake was made on moving the variable to the left side.

• The mistake was made on moving the constant to the right side.

Multiple Choice

Is there a mistake on the equation solved? If so where was the mistake made?

• This equation is solved correctly.

• The mistake was made on the distributive property step on the left side.

• The mistake was made on combining like terms on the left side.

• The mistake was made on moving the variable to the left side and constant to the right side.

• The mistake was made on the distributive property step on the right side.

Multiple Choice

Is there a mistake on the equation solved? If so where was the mistake made?

• This equation is solved correctly.

• The mistake was made on the first step of moving the variable to the right side.

• The mistake was made on the second step of moving the constant to the left side.

• The mistake was made on the last step when isolating the variable by removing the coefficient