Multi Step Equations

Multi Step Equations

Pre-Algebra

Poll

What is your favorite operation?

• Addition

• Subtraction

• Multiplication

• Division

Poll

Would you rather not have a microwave or not have a toaster

• No microwave

• No toaster

​What we've been doing....

​The past couple weeks, we have been solving one and two step equations. In these equations, we only needed to use 2 inverse operations to solve for variable. Lets take a look at some of these.

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$x+6=-4$  

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$x-5=-8$  

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$-4x=20$  

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$\frac{-r}{8}=-7$  

​Great job!

​These are one step equations. It only took one inverse operation to solve each of these equations.

​

​Now, we can combine these into 2 step equations. In the following problems, we will practice 2 step equations.

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$2x+5=13$  

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$\frac{r}{7}-8=-5$  

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$\frac{g-6}{4}=-3$  

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$\frac{t-8}{-5}=-4$  

​There are two more rules we've discussed that help us solve what we call "Multi-Step Equations"

​1. The Distributive Property

​a(b+c)=ab+ac.

​

​When we have a number outside of parentheses, we multiply that number into each part of the parentheses.

​

​Lets practice some!

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$2\left(x-5\right)$  

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$-3\left(-2x-7\right)$  

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$-8\left(7x-10\right)$  

​Combining Like Terms

​Our other move is Combining Like Terms.

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​Like terms have the same variable part.

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​3x and 4x ARE like terms

​3x and 4xy ARE NOT like terms

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​12 and -5 ARE like terms

​10x and -5 ARE NOT like terms

Multiple Choice

Are 3x and -10x like terms?

• Yes

• No

Multiple Choice

Are 6xyz and -7xy like terms?

• Yes

• No

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Are -3/4 and 1000 like terms?

​Combining Like Terms

​To Combine Like Terms, we have to combine the coefficients of the terms.

​2x+4x=6x 8xyz-10xyz=-2xyz

​

​-2y+6y=4y 7x+5-2x=5x+5

​

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Combine Like Terms: 2x+3x

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-6xyz+12xyz

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5z+9-7z

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2x+5y+8x+10y

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-8x+2x

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15z+12y+6x-4x-10y-15z

​Multi-Step Equations

​What do we see here? What part of this equation should we consider? How can we make this simpler?

​Step 1: Use the Distributive Property

​Step 2: Combine Like Terms

​Step 3: Solve the Two Step Equation

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Apply the distributive property to simplify 6(x+3)

How can we combine like terms here?​

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$6x+18-4x+1=43$  How can we combine like terms here?

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Solve  $2x+19=43$