Algebra 1: Solving Equations with variables on BOTH sides

Do Now

Solve the following equations:

2x+5=88x+2x+5=102x+3=5x16 – x = 12 – 3x

Do Now Answers:

2x+5=8Answer: x = 3/2

8x+2x+5=10Answer: x = 1/2

2x+3=5xAnswer: x = 1

16 – x = 12 – 3xAnswer: 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) + (22)= 5x + 2 * 6