Solving Multi-Step Equations

Solving Multi-Step Equations

by Kevvin Hankins

​Standards

​MGSE7.EE.3 Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) by applying properties of operations as strategies to calculate with numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.

​Learning Target

​K1: I can apply the order of operations to perform multi-step arithmetic calculations.

Poll

Can you solve one step equations?

• Yes

• No

• Maybe

• What's a one-step equation?

Draw

Solve this problem: 4x = 36

Open Ended

What is the first step in solving this problem: 5X + 5 = 6

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Solving Multi-Step Equations

2021

An Equation is a statement that says both sides of the equal sign are equivalent, or the same.

Here are the steps in solving a multi-step equation:

• Distributive Property

• Combine like terms (on the same side of the equation)

• Use inverse operations to put variables and constants on opposite sides of the equation.

• Isolate the variable

Multiple Choice

What is the first thing you should do to simplify an equation?

• add

• Distributive Property

• Combine like terms

• divide

How can you tell that you need to use the Distributive Property? You will see a term sitting next to parentheses, ready to be multiplied to the terms inside the parentheses. Like these:

• 4(x-7)=-9

• -8x+3=2-8(x+4)

Multiple Select

Which of the following equations require you to use the Distributive Property first?

Select all that apply.

• 6x-8=7(x+2)

• 7n-5=3

• 2(a-9)=9a+1

• 4-9y=8+4y-2

Multiple Choice

Let's Practice using the Distributive Property.

6(x-3)

• x-18

• 6x+18

• 6x-18

• 6x-9

Multiple Choice

-3(n-8)

• 3n-8

• -3n-24

• -3n+24

Once you distribute, check to see if you have like terms, on the same side of the equal sign. Here are some examples of like terms:

• 5x and -6x

• -6 and 3 ***Remember that constants (regular numbers) are like terms with each other.***

• 7m and m

Multiple Select

Check the boxes that show like terms.

• 5 and -8

• 4n and -8x

• -9 and 9x

• 1 and 7

• 6y and 8y

Multiple Choice

Let's practice combining like terms.

7x-8+3x-1

• 10x-9

• 21x+8

• 4x+9

• 10x+9

Once you distribute and combine like terms, make sure variables are on one side and constants (regular numbers) are on the other side. Use inverse operations to move terms to the other side.

Multiple Select

If we wanted to move variables to one side, what operations could we do to accomplish this?

(2 answers)

7x-8=-5x+3

• Subtract 7x from both sides

• Add 8 to both sides

• Subtract 3 from both sides

• Add 5x to both sides

Multiple Choice

Once you have variables on one side, collect the constants on the other side. What operation should we use to collect the constants on the opposite side of the variable?

-5=4x-3

• Add 5 to both sides

• Subtract 4x from both sides

• Add 3 to both sides

• Subtract 3 from both sides

Here is an example of how to solve a Multi-Step equation. See if you can follow the steps that are written on the side.

Multiple Choice

Find the solution to the following equation

9n+1=5(n-6)-1

***Use scratch paper.

• n=8

• n=-8

• n=2

• n=-2

Poll

How confident do you feel in being able to solve a multi-step equation?

• Very Confident

• Somewhat confident

• Not that confident

• I'm lost