# Algebra 1: Solving Equations with variables on BOTH sides.

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Algebra 1: Solving Equations with variables on BOTH sides

Do Now Solve the following equations: 2x+5=8 8x+2x+5=10 2x+3=5x 16 – x = 12 – 3x

Do Now Answers: 2x+5=8 Answer: x = 3/2 8x+2x+5=10 Answer: x = 1/2 2x+3=5x Answer: x = 1 16 – x = 12 – 3x Answer: x = -2

Equations vs. Expressions What’s the difference?

Expressions vs. Equations Equations: Have an equals sign! They can be solved. Examples: y+2=x 5+x=9 Expressions: Do not have an equals sign. They can only be simplified. Examples: 2x+3y 5y+2y+8

Solving Equations Steps: Simplify the left side of the equation Simplify the right side of the equation CLT (Combine Like Terms) Solve!

Example 1: 2x + 4x + 4 + 6 = 12 + 3x + 5x + 14

Checking Solutions You can easily determine whether you are right by substituting your solution back into the original equation! We got x = - 8. So let’s see if it works! 2x + 4x + 4 + 6 = 12 + 3x + 5x + 14

4x + x + 2 = 5x – 4 + 6 Example 2:

WHAT?!?!?! We Got that x = x. So what is our solution?!?!

Example 3: x + 4x + 2 + x = 6x

WHAT?!?!?! We got 0 = 2? What’s the solution to this problem?

Notice….. Equations can have three types of answers: One Solution Infinitely Many Solutions No Solutions

Practice Try some on your own!

Exit Ticket Solve the following problem– how many solutions does it have? x + x + x + 3x + 8 + (2 * 6) + (2 2 )= 5x + 2 * 6

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