Vocabulary

• Variable - the letter that represents an unknown value ex. y, x, n

• Coefficient - The number infront of the variable ex. 6x, 7y, 1n

• Constant - Any number being added or subtracted in the expression ex. 6 + 1 - 2

• Terms - All the variables with their coefficient and constants that create an expression ex. 3 + 2x + 4y + 1 + 6x This expression has 5 terms.

• Like Terms - same variable to the same power

Combining Like Terms

AKA simplifying expressions

Expressions vs Equations

Before solving an equation, it is helpful to simplify each expression.

We simplify by combining like terms... but what does that mean?

One-Step Equations

Solving equations

• use inverse operations to isolate the variable

• keep the equation balanced by performing the same operation on both sides of the equals sign

3 = z + 6

• subtract 6 from both sides

• z = -3

-16 = -4p

• divide both sides by -4

• p = 4

k/3 = -30

• multiply both sides by 3

• k = -90

Two Step Equations

How to Solve

• Get rid of the 3rd Wheel: Add or Subtract to get rid of the number

• Break up the happy couple: Multiply or Divide both sides of the equation by the coefficient

Multipstep Equations

1) Distribute

2) Combine like terms

3) complete two step equation steps

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Equations with variables on both sides

Now we only have the variables on one side

We can move on to solving equations like you are used to

By removing the constants (on both sides) so that we have the variable (x) by itself

We conclude that each x (rectangle) is the same as 4

Remember

• The goal is to have the variables on one side

• We remove as many as we can from both sides

• Once there are variables only on one side, continue solving for x

How Many Solutions?

A review of the 3 types of solutions to equations

Infinitely Many Solutions

• True mathematical statement

• Example 3=3

• The coefficients on the variables will be the SAME on both sides of the equation, and the remaining numbers to be the SAME.

• Example: 4x+15=4x+15

One Solution

• Solve for the variable, ends with the variable equal to ONE number.

• Ex. x=3

• The coefficients on the variables will be DIFFERENT

• Ex. 5x+30=7x+30

No Solution

• Ends with a FALSE mathematical statement

• Ex. 4=8

• The coefficient on the variable will be the SAME, much like with a true statement. But, the remaining numbers will be DIFFERENT.

• Ex. -7x+10= -7x+15