Expressions and Equations Homework

• 5x + 5

Answer explanation

Remember that you can check all of these possible answers ... and choose the expressions that match when you evaluate for a value of x. Try it...and look what happens when you use x=1 ... you will see why I never do this.

• 12(4x - 72)

• 8(6x - 9)

• -12(6 - 4x)

• -6(-8x + 12)

• 24(2x + 3)

Answer explanation

Which strategy did you use? When applying the distributive property...make sure you use the box method and multiple the outside term by both terms in the parenthesis. I used Desmos to check...here is a screen shot that has one good selection...and one incorrect selection.

Choose three expressions that match the algebra tiles model shown. The preferred method is to understand that the model shows three (3) groupings of (3x-2) ... and select the expression that can be simplified using distributive property. Then simplify it to find another matching expression. Finally...choose a large expression that literally spells out each of the three groups...it will have 6 terms. In a pinch...well...three of the expressions should evaluate to equal values...choose x=9 and find the three that evaluate to the same value using Desmos.

• 3(3x - 2)

• 3(3x + 2)

• 9x - 6

Answer explanation

Just be safe and check this one using Desmos. Be very careful to type in the expression correctly. Make sure the fractions and variables are placed in the right spot. Don't allow the variable to creep into the denominator of a fraction. The screen shot has a correct answer option and an incorrect one.

Find the value of  x  in the equation modeled by the algebra tiles.

Hint...write down the equation...use the key. There are variables on both sides. Solve the equation using our 5 steps...or use the L-R strategy in Desmos. Either way...check in Desmos.

NOTE: Only type in a number...not the x= part.

Answer explanation

The equation modeled is

4x - 2 = 2x + 4

...solve how you will...the Desmos check verifies that x = 3.

• -6

• 9

• -9

• 13

Answer explanation

Solve using our steps...or check the possible answers. Here is my Desmos screen shot.

Answer explanation

Here is my Desmos screen shot...

Four friends are going to the Herndon Carnival. The entrance fee is $10 each and each ride ticket costs $2. Each friend bought the same number of ride tickets and the group spent $88 all together. 

 

Let x  represent the number of ride tickets. 

 

Which equation could be used to find how many ride tickets each friend bought?

Hint: This screams for a distributive property model because there are 4 friends spending the same amount of money. Usually I tell students to look for the words "each, every, or per" and say that the near by numbers need a variable. However, this time you are told that x is the number of tickets each friend purchased. So...the 2 gets the variable and the total is "=88" ... choose one equation below:

• 4(2x + 10) = 88

• 4(10x + 2) = 88

• (2x + 10) + (2x + 10) = 88

• 2x + 10 = 88

Answer explanation

There are 4 friends, and they each spent $10 to get in the carnival...a one time charge for each friend. Then each rode the same number of rides, and spent $2 per ride (ticket). So each friend spent:

2x + 10 .... but there are 4 friends. The total spent was $88 .... so we need 4 groups of (10+2x)...

4(2x + 10) = 88

Answer explanation

Here is my Desmos screen with a check. The only thing that can go wrong is to have a typo. Needed to change directions and be patient too.

The Lopez and Jones families spend the same amount of money at the movies ("equal" amount).

• The Lopez family buys 6 tickets and spends $46 on snacks. 

• The Jones family buys 4 tickets and spends $72 on snacks.

 

They represent the situation with the equation  6y + 46 = 4y + 72  and find that  y=13 .

 

What does  y=13 mean in this situation? Hint: the problem does not state what y represents...but look where it is...next to the number of movie tickets each family purchased. The problem also talks about the money spent...and each family spent more that $13 on snacks alone.

• Each family spent $13 total.

• Each family purchased 13 tickets

• Each movie ticket cost $13

• The movie started at 13:00 military time, which is 1pm

Answer explanation

y is the cost per ticket...each ticket cost $13. Think about this...each family spent money on tickets and snacks. We know how much they spent on snacks. We know how many tickets each family bought. We know that each family spent the same (=) amount of money. The only thing we didn't know was how much a ticket cost.