Unit 9 Mock Test

Jen has at least $2 in her pocket. What graph and inequality represent the amount of money, m, that is in Jen's pocket? Select all that apply.

• First Graph

• Second Graph

• Third Graph

Answer explanation

"at least" is a key word that represents "greater than or equal to".

Because it is also "or equal to", it is including the number 2. To represent this, you use a closed circle on the graph. Numbers that are "greater" are to the right of a number, so that is why you shade right.

Determind which value makes the equation 30 = 8x - 2x true.

{24, 12, 6, 5}

Answer explanation

1. You need to combine the like terms of 8x -2x to become 6x.

2. Then, you are looking at 30 = 6x.

3. Use inverse operation of multiplication to undo the 6 and x, which is division. You will divide 6 on both sides (what you do to one side, you do to the other)

4. You'll be left with 5 = x, which can be re-written as x = 5.

Determine which value(s) make the inequality x + 8 < 12 true.

• -5

• -3

• 4

• 6

• 8

Answer explanation

1. Solve the inequality using inverse operations.

2. It would become x < 4, but it does not include 4. Any answer choice less than 4 would be acceptable.

Another method:

1. Plug in each value for x and see if it makes a true statement.

Brian is playing a game with cards that have positive and negative numbers on them. For his next move, he has to add the two cards he is given.

He gets one card.

He gets a second card that has a value of 12. If the sum of Brian's two cards is 3, what was the number on the first card?

Answer explanation

The SUM (answer to an addition problem) is 3. The second card is 12. This can be represented as: x + 12 = 3

You can solve this equation with the inverse operation of addition (subtraction) of 12 from both sides. That way, x will be isolated.

This will result in x = -9

For the verbal description given, choose the correct mathematical equation: “A number minus 5 is negative 3.” Also, select the solution.

• 5 - x = -3

• x - 5 = -3

• x - 3 = -5

• 8

• 2

Answer explanation

"A number minus 5 is negative three" is taking some unknown number and removing 5 from it, not the other way around.

"Is" is a key word for "equals".

x - 5 = -3

Solve the equation by adding 5 to both sides of the equal sign.

x = 2

Answer explanation

Solve using the inverse operation of what you are trying to get rid of!

You want to get rid of the "divided by 4" so that the variable can be isolated. To undo "divided by 4", you need to multiply by 4.

Whatever you do to one side, you have to do to the other, so 16 will also be multiplied by 4.

The 4s will cancel out, leaving:

x = 64

Cameron bought a total of 8 large pretzels for himself and his friends. He spent a total of $16. Let p represent the price of one pretzel. Which equation represents this situation?

• 8p = 16; p = 2

• 8p = 16; p = 8

• 16p = 8; p = 2

• 16p = 8; p = 8

Answer explanation

You would calculate this cost by taking the cost of one pretzel times the number of pretzels bought. This is represented as 8p since there were 8 pretzels bought, but the cost of one is not given (variables are used as placeholders).

It tells us he spent 16, so the situation can be represented as: 8p = 16

Then, you have to solve using inverse operations. Divide 8 on each side, giving you:

p = 2

Plug 2 back into the equation to check!!

Solve the equation 12.3 = 4.1m

• 0.03

• 0.3

• 3

• 30

Answer explanation

Your goal is to isolate the variable!!!!!

Use the inverse operation of what is currently happening to the variable. In this case, since multiplication is happening, we need to divide by 4.1. The 4.1s will cancel out.

Whatever you do to one side, you do to the other. 12.3 divided by 4.1 is 3.

So, 3 = m or m = 3

Check your answer by plugging it back in!!!

Answer explanation

Turn the mixed number to an improper fraction.

Find a common denominator (10). Re-write 1/5 as 2/10.

Use inverse operations to solve. Subtract 2/10 from both sides.

Turn your answer back into a mixed number.

Plug your answer back into the equation to check!!!!

You have a certain amount of money, m, in your bank account. You spent $17.50 at the store but still have at least $42 in your bank account. Write and solve an inequality that represents this situation.