Solving multi-step equations!

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Solving Equations! ( aka solving a mystery!)

What are one step equations? How do they look? What are the four basic operations?

One step means you have to do only one thing to find an answer! Oh, to stay that simple!

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One Step Equations

What are the four basic operations?

Add

Subtract

Multiply

Divide

How does an equation with addition look?

y + 14 = 20 How is the 14 connected to the y? (added) What is the opposite of add ? (subtract)

so to solve start with the 20 on the other side, and subtract 14 from it

20 - 14 = 6

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How does an equation with subtraction look?

x - 120 = 80 How is the 120 connected to the x? (subtracted) What is the opposite of subtraction? (addition)

To solve, start with the 80 on the other side and add 120 to it!

80 + 120 = 200

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How does an equation with multiplication look?

3n = 12 How is the three connected to the n? (multiplied) What is the opposite of multiplication? (division)

So, to solve this equation, go to the other side and start with the 12

take the 12 and divide it by 3

12 divided by 3 = 4

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How does an equation with division look?

k/2 = 16 How are the k and the 2 connected? (divided) What is the opposite of division? (multiplitication)

so, to solve this equation, go to the 16 on the other side, multiply it by the 2

16 times 2 = 32

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How do two step equations look? What makes them different? (besides another step????)

The difference is the variable term has now been multiplied or divided AND also has a number either added to or subtracted from it

Examples: 2x + 4 3x - 5 x/6 + 2 x/4 - 6

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In the picture below, how is the x combined with the 9? How is the 3 combined with the 9x?

In the picture below, how is the x combined with the 3? How is the 12 combined with the variable term?

IMPORTANT!!!! In two step equations, take care of anything added to or subtracted from first!!!!!

9x + 3 = 21 What is added (or subtracted) from the variable term? (3 is added)

So, the first step to solve is to take the 3 to the other side (change sides, change signs)

Then you have 9x = 21 - 3

Now do the math for the like terms. What is 21 - 3? (18)

Now my equation is 9x = 18

How are the x and the 9 put together? (multiplied) What is the opposite of that? (divide)

To finish, take the 18 on the other side and divide it by 9

18 divided by 9 = 2

x/3 - 12 = 36 What is connected to the variable term? (minus 12) What is the opposite of that? ( plus 12)

So, take the 36 on the other side and add 12 to it

36 + 12 = 48

Now how are the x and the 3 put together? (divided) What is the opposite of that? (multiply)

Take the 48 on the other side and multiply it by 3

48 times 3 = 144

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More than Two Steps!

look for parenthesis to see is you need the distributive property

if you see them, distribute ( which means multiply two times)

once you multiply, check for like terms (what does that mean?)

combine like terms ON THE SAME SIDE FIRST - if you have any SAME SIDE KEEP SAME SIGN ALREADY THERE

combine like terms on opposite side SECOND - CHANGE SIDES CHANGE SIGNS

the last step will be to divide or to multiply

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EVEN MORE STEPS

look for parenthesis to see is you need the distributive property

if you see them, distribute ( which means multiply two times)

once you multiply, check for like terms (what does that mean?)

combine like terms ON THE SAME SIDE FIRST - if you have any SAME SIDE KEEP SAME SIGN ALREADY THERE

combine like terms on opposite side SECOND - CHANGE SIDES CHANGE SIGNS

the last step will be to divide or to multiply