Final Exam Review| Equations

Final Exam Review| Inequalities and Equations

Let's do it

Multiple Choice

Simplify:

3x + 2y - 5x + y

• -2x + 3y

• 8x + 3y

• 5xy

How do you multiply a number by a variable?

• To multiply a number by a variable, remember there is always a 1 in front of that variable if the variable is alone. 4(x)= 4x It is like multiplying 4 times 1x

Multiple Choice

7(x)=

• 7x

• 7+x

Multiple Select

4(a + 3)

• 4a + 3

• 4 + 3

• 4a + 12

• a + 12

Fill in the Blank

5 + 9(x+2)

First I must________ 9 times x and 9 times ___ then. Last I add the 5 and ______.

What is an equation?

• Equation: an algebraic sentence with an equal sign

• The goal of Solving Equations: to isolate the variable (get it by itself)

• To Isolate the Variable: Use Inverse Operations! (do the opposite!)

• Justify Your Work: Properties of Equality

One-Step Equations

These are equations you can solve in one step by doing the OPPOSITE operation.

Multiple Choice

Solve x + 6 = 10

• 10

• 6

• 4

• 16

Multiple Choice

Solve

 $\frac{x}{4}=12$  

• 4

• 3

• 12

• 48

Multiple Choice

Laurie rode her bike 17.5 miles in 2 hours. She uses this equation to represent the relationship between her time and distance.

2x = 17.5

What does the solution x= 8.75 represent?

• The distance Laurie rode her bike.

• The time Laurie spent riding her bike.

• The distance Laurie traveled per hour.

• Not here

Two Step Equations

• These are equations that you can solve in two steps

• Typically, the FIRST step is to take care of any addition or subtraction

• Tyipcally, the SECOND step is to take care of any multiplication or division

• There are SOME cases where the steps may be different, but that is usually if you have exponents, parentheses, or a BIG division problem

Multiple Choice

Solve 8 + 4x = 24

• 2

• 4

• 8

• 24

Multiple Choice

Solve

 $\frac{x}{2}-11=13$  

• 4

• 48

• 24

• 12

Multiple Choice

Greg wrote in his math journal that 17 - x = 9 is an example of an algebraic equation. Which statement is true about the example Greg wrote in his math journal?

• Greg's example is an equation because there is a variable present.

• Greg's example is an equation because it is a number sentence stating two amounts are equivalent.

• Greg's example is an equation because x can represent any value.

• Greg's example is an equation because there are two numbers present.

Multi Step Equations

• DISTRIBUTE first

• COMBINE second

• Get x's on one side

• SADME to finish

Multiple Choice

Solve 2x + 3x - 6 = 14

• 20

• 10/3

• 4

• 14

Multiple Choice

Solve -4(3x - 6) = 48

• -6

• -2

• 2

• -12

Multiple Choice

Solve (HINT - take care of the division FIRST, then the addition)

 $\frac{x+4}{7}=8$  

• 52

• 60

• 28

• 84

Multiple Choice

Challenge Question: Solve 10 - (4x - 3) = 2x - 7

• 10/3

• 7/3

• 5/2

• 17