Unit 5: Solving Equations
Evaluating Expressions (Order of Operations: PEMDAS)
Inverse Operations & Solving 1-Step Equations (SADMEP)
solving_1step.pdf |
1step.pdf |
Solving 2-Step Equations
solving_2step.pdf |
2step1.pdf |
Click HERE to see how to visually represent and solve an equation with a variable. (From Illustrative Mathematics)
2step2.pdf |
Combining Like Terms
combining.pdf |
Distributive Property
solving_distributive.pdf |
s1ve_distributive.pdf |
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Solving Equations with Variables on Both Sides
- 3Remember that to solve multi-step equations, you should:
Step 1. Distribute
Step 2. Combine
After that, you'll (most likely) have a 3-step equation where there are variables on both sides.
Take the example 2x + 3 = 7x - 7
Step 3a would be to get all of the x's on one side. Let's make a rule to get all x's on the left side of the equals sign.
To eliminate the +5x on the right, we need a -5x on both sides.
2x + 3 = 7x – 7
–7x –7x
-5x + 3 = – 7
At this point, we're at a two-step equation! Step 3b would be to get all of the integers on the right side.
To eliminate the +3 on the left, we need a -3 on both side.
-5x + 3 = –7
– 3 – 3
-5x = -10
Now we're left with a one-step equation because the only thing left to do is eliminate the coefficient of x.
We eliminate coefficients with division because coefficients represent multiplication, so we'll divide both sides by –5.
–5x = –10
–5 –5
The –5's on the left cancel, leaving x. The –10/–5 on the right simplifies to 2.
Therefore:
x = 2
Step 1. Distribute
Step 2. Combine
After that, you'll (most likely) have a 3-step equation where there are variables on both sides.
Take the example 2x + 3 = 7x - 7
Step 3a would be to get all of the x's on one side. Let's make a rule to get all x's on the left side of the equals sign.
To eliminate the +5x on the right, we need a -5x on both sides.
2x + 3 = 7x – 7
–7x –7x
-5x + 3 = – 7
At this point, we're at a two-step equation! Step 3b would be to get all of the integers on the right side.
To eliminate the +3 on the left, we need a -3 on both side.
-5x + 3 = –7
– 3 – 3
-5x = -10
Now we're left with a one-step equation because the only thing left to do is eliminate the coefficient of x.
We eliminate coefficients with division because coefficients represent multiplication, so we'll divide both sides by –5.
–5x = –10
–5 –5
The –5's on the left cancel, leaving x. The –10/–5 on the right simplifies to 2.
Therefore:
x = 2
Click HERE to check out Khan Academy's videos and practice problems about this topic!
Solving Multi-Step Equations
solving_multistep1.pdf |
solving_multistep2.pdf |
solving_multistep3.pdf |
solving_multistep4.pdf |
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Number of Solutions ( 1 / 0 / ∞ )
numberofsolutions1.pdf |
ANSWERS TO THE ABOVE PROBLEM SET
1 Solution:
No Solution:
Infinite Solution:
1 Solution:
No Solution:
Infinite Solution:
This video has a focus on infinite (∞) solutions––when the left side and the right side are the exact same.