Exam Review- Fall 2021- Algebra I Day 1

Exam Review- Fall 2021- Algebra I Day 1

by Katie Argall

​Today: Units 1-2

• ​Classifying #s

• ​order of operations

• ​phrases to expressions

• ​properties

• ​expression values

• ​multistep equations

• ​absolute value equations

• ​literal equations

• ​inequalities

Multiple Choice

Which statement is NOT true?

• Every rational number is a real number.

• Every counting number is a whole number.

• Every integer is a rational number.

• Every decimal number is an irrational number.

Multiple Choice

What is the best classification for this number?   -4

• natural
• whole
• integer
• rational

Multiple Choice

Classify the number -2.5

• Real, rational

• Real, rational, integer

• Real, irrational

Multiple Choice

What is the best classification for this number?  
π

• integer
• rational
• irrational
• imaginary

Multiple Choice

What is the best classification for this number?  .78787878...

• integer
• rational
• irrational
• whole

Multiple Choice

40+(72÷9)÷8

• 49
• 25
• 41
• 15

Multiple Choice

Solve the following:
(2 + 7 - 1) ÷ 2²

• 16
• 2
• 72.25
• 8.75

Multiple Choice

Translate: 35 multiplied by the quantity of r plus 45

• $$35\left(r+45\right)$$  

• $$35r+45$$  

• $$35\cdot r+45$$  

• $$\frac{35}{r+45}$$  

Translating Phrases

Multiple Select

Which demonstrates the commutative property? Select all that apply.

• $$8+9=9+8$$

• $$\left(4\cdot2\right)3=3\left(4\cdot2\right)$$

• $$9-4=4-9$$

• $$2\cdot3\cdot5=2\cdot5\cdot3$$

• $$8\div4=4\div8$$

Multiple Choice

$$\left(4\cdot6\right)\cdot5=4\cdot\left(5\cdot6\right)$$  represents what property?

• Commutative property of multiplication

• identity property of multiplication

• associative property of multiplication

• zero property of multiplication

Multiple Choice

Which property is represented below?
15(1) = 15

• Identity
• Commutative
• Associative
• Inverse

Algebraic Properties of Equality

We use the word Equality when there is an = sign.

Multiple Choice

8v - 4(v + 8) = 8

• 2
• 10
• 4
• -4 

Multiple Choice

Solve for x.

• 55
• 60
• 15
• 35

Multiple Choice

What is the first step in solving the equation 2a - 4(a - 5) = 10

• Add 4 to both sides
• Add the 2a and a 
• Distribute 4 to a and -5
• Distribute -4 to a and -5

For your notes: Solve Equations by ISOLATING the variable

• 1 undo addition or subtraction

• 2 undo multiplication or division

• The exception ... a GIANT fraction!!

Multiple Choice

What is the absolute value of -5?

|-5| = ?

• -5

• 5

• +(-5)

• -5 and 5

Multiple Choice

Solve for X

|X|=7

• X= 7

• X= -7

• X= 7 and X= -7

• No Solution

Multiple Choice

Solve for X

|X| = -3

• X= 3 and X= -3

• X= 3

• X= -3

• No Solution

Absolute Value Equations

with review

It is very important to isolate the Absolute value equation before attempting to solve.

Think of the absolute value equation as a variable when performing operations to get it isolated. Notice we add 10 to both sides then divide both sides by 3 to get |x-2| isolated. Now the problem |x-2| = 7 can be solved like we just learned.

Multiple Choice

What would be the correct setup for solving for X?

|X+3| = 5

• X+3= 5 and X+3= -5

• X+3= 5 ad X-3= 5

• X+3= -5 and X-3 = -5

• X+3= 5 and -X-3= -5

Multiple Choice

Solve for X

2|X+3|+3=1

• X= -4 and X= -2

• X=2 and X= -2

• X=0

• No Solution

Multiple Choice

Which inequality is represented by the following graph

• x < -8

• x > -8

• x ≥ -8

• x ≤ -8

Graphing Inequalities

• When graphing your inequality on the number line, the open circle means the number is not included.

• When graphing your inequality on the number line, the closed circle means the number is included.

Multiple Choice

$$2\left(x-3\right)+9\ge x$$  

• $$x\ge-6$$  

• $$x\ge15$$  

• $$x\le-3$$  

• $$x\ge-3$$  

• $$x\le-6$$  

What is interval notation?

Multiple Choice

Look at the Graph. Write the inequality in interval notation.

• [-4, -1)

• (-4, -1)

• (-4, -1]

• [-4, -1]

Multiple Choice

Solve and graph:

• A

• B

• C

• D

Multiple Choice

Solve for C

$$\frac{ca}{k}+e=s$$  

• $$c=aesk$$  

• $$c=\frac{kes}{a}$$  

• $$c=\frac{k\left(s-e\right)}{a}$$  

• $$c=\frac{\left(s-e\right)}{ak}$$  

Absolute value represents the distance from 0 on a number line.

Any measurement is always positive, including distance. you can't run a negative mile, even if you run it backwards, you still ran the mile.

The Vertical lines you see here surrounding -3 means Absolute Value in Math.

You can remove those vertical lines by changing what is inside them to a positive value. Easy enough for constants(numbers) right? try it.

Multiple Choice

What is the absolute value of -5?

|-5| = ?

• -5

• 5

• +(-5)

• -5 and 5

We can also take the absolute value of a variable.

Just like solving for A in an equation, we can do the same for |A|. remember that the value inside the absolute value symbols is the distance from 0. So you can see A=5 if we travel 5 places to the right. Notice if we travel 5 places to the left, we arrive at -5. So A can equal both -5 or 5, depending on what direction we travel.

How would this math problem look originally? |a| = 5

So when we solve for a, we see if a=5, then |5| also equals 5. We also see if a= -5 that |-5| = 5. We can see that when taking the absolute value of a variable, we will have 2 answers; the answer for moving right(towards positive numbers) and the answer for moving left(towards negative numbers).

Notice we have the absolute value of Y equaling -5.

If we want to solve this like the one before, would we say Y= 5 or -5??? Let us try and see.

y=5 then |5| = -5. That does not seem right, because |5| = 5 not -5. What about if y= -5 then |-5| = -5, that also is not right, because

|-5| = 5. So y has no solution because an absolute value can never equal a negative number. You try some.

Multiple Choice

Solve for X

|X|=7

• X= 7

• X= -7

• X= 7 and X= -7

• No Solution

Multiple Choice

Solve for X

|X| = -3

• X= 3 and X= -3

• X= 3

• X= -3

• No Solution

Notice when solving for X, we have a positive value for A and a negative value for A.

We can apply this process to more advanced absolute value equations.

The equation |X-5|=2

Notice that we have setup two equations. Both equations have the absolute value symbols removed. But one of them has the value switched to a negative. This is how we find out the distance, one going left and one going right from our starting point on a number line. We solve both equations by isolating the variable, just like we have done before. Both equations are solved by adding 5 to both sides. We have our two answers for X; X=7, X=3.

It is very important to isolate the Absolute value equation before attempting to solve.

Think of the absolute value equation as a variable when performing operations to get it isolated. Notice we add 10 to both sides then divide both sides by 3 to get |x-2| isolated. Now the problem |x-2| = 7 can be solved like we just learned.

Why do we isolate the absolute value part first?

Since absolute value is always a positive number, we need to make sure that the equation makes since. Notice in the picture as we start isolating the absolute value part that we end up with |x+2| = -2/3.

Since an absolute value can not equal a negative number, there would be no solution. try some,

use paper and pencil as needed.

Multiple Choice

What would be the correct setup for solving for X?

|X+3| = 5

• X+3= 5 and X+3= -5

• X+3= 5 ad X-3= 5

• X+3= -5 and X-3 = -5

• X+3= 5 and -X-3= -5

Multiple Choice

What would be the correct way to write the problem before solving?

2|x-1|-6=4

• |x-1|=5

• x-1=5

• |x-1|=-5

• x-1=-5

Multiple Choice

Solve for X

2|X+3|+3=1

• X= -4 and X= -2

• X=2 and X= -2

• X=0

• No Solution