Chapter 10a

Chapter 10

This chapter is all about combining like terms.

There are 8 lessons and a test. We will do 5 lessons this week and the rest next week.

The vocabulary assignment will open this week and be due at the end of next week, but I do advise that you complete it before the test.

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Lesson 80 - Fancy Distance Problems

Like Terms

Lesson 76 - Adding x's

4x + 2x = 18

By combining the x's we are simplifying the equation to make it easier to solve.

Let's look at an example.

The numbers that are multiplied by the x's are called coefficients.

Multiple Choice

Simplify the expression 3x + 9x, and choose the best choice:

• 12x

• 6x

• 3x

• 27x

• -12x

Multiple Choice

Simplify the expression 8x + 6x = 28, and choose the best choice:

• 14 + x = 28

• 14x

• 14x = 28

• 8 + 6 + x = 28

Multiple Choice

Some equations need to be simplified by adding x’s (instead of numbers).

• True

• False

Multiple Choice

A number multiplied by an x is called a “coefficient.”

• True

• False

Multiple Choice

To add (combine) x’s, you just add their coefficients.

• True

• False

Math Response

6x+4x=10

Type answer here

Correct Answer: 1

Deg^°

Rad

Math Response

1x+2x+9=-33

Type answer here

Correct Answer: -14

Deg^°

Rad

8x - 3x = 15

We just subtract the numbers like normal. Even if they are negative.

​Subtracting Coefficients

Lesson 77 - Subtracting x's

Multiple Choice

To subtract x’s, you subtract their coefficients.

• True

• False

Multiple Choice

Another way to subtract x’s is to change the subtraction to addition of the opposite first.

• True

• False

Multiple Choice

Simplify each expression below. Select the best possible choice.

13x - 5x

• 18x

• -18x

• 8x

• -8x

• -45x

Multiple Choice

Simplify each expression below. Select the best possible choice.

-6x - 4x

• -6x

• 2x

• -10x

• -2x

• 10x

Math Response

33x - 16x = 51

Type answer here

Correct Answer: 3

Deg^°

Rad

Math Response

-8x - 6x = -70

Type answer here

Correct Answer: 5

Deg^°

Rad

2x + x = -24

x by itself doesn't have a coefficient, but we can assume there is a 1 there. We can do this because any number multiplied by 1 is still the same number.

x = 1x

Lesson 78 - x and 1x

Multiple Choice

Simplify each expression below. Select the best possible choice.

x + 6x

• -7x

• 5x

• 6x

• -5x

• 7x

Multiple Choice

Simplify each expression below. Select the best possible choice.

13x - x

• -14x

• 14x

• 12x

• -12x

Multiple Choice

You can change a single x to 1x in order to use the adding coefficients shortcut.

• True

• False

Multiple Choice

You can change a -x to -1x in order to use the adding coefficients shortcut.

• True

• False

Math Response

-6x - 3x = 45

Type answer here

Correct Answer: -5

Deg^°

Rad

Math Response

7x - x = 36

Type answer here

Correct Answer: 6

Deg^°

Rad

3x + 4x = 21

Gina can paint 3 porcelain dolls per hour and Rosalie can paint 4 porcelain dolls per hour. How long will it take the two of them working together to paint 21 dolls? In this equation x stands for the number of hours to paint the dolls.

Lesson 79 - Work Problems

Multiple Choice

Alex can read 36 pages per hour and Jaci can read 44 pages per hour. How many hours will it take them to read 240 pages?

Choose the equation that best represents this problem.

• 36+44+x=240

• 36x+44x=240

• 240-36-44=x

• 80+x=240

Multiple Choice

Brittney can bake 7 cakes per hour and Ed can bake 5 cakes per hour. How many hours will it take them to bake 48 cakes?

Choose the equation that best represents this problem.

• 48-7-5=x

• 12+x=48

• 7x+5x=48

• 48-x=12

Multiple Choice

Work problems usually translate into an equation with more than one x.

• True

• False

Multiple Choice

In a work problem, the rate multiplied by the time equals the total amount of work a person does.

• True

• False

Lesson 80 - Fancy Distance Problems

Hal and Larry are headed straight toward each other. Hal is driving at a safe speed of 55 mph, but Larry is driving recklessly at a speed of 75 mph. If the two are 260 miles apart, how many hours will it be before they meet (assuming Larry can keep his car on the road)?

55x + 75x = 260

Multiple Choice

Driver #1 and driver #2 are headed straight toward each other. Driver #1 is driving at 65 mph, and driver #2 is driving at 55 mph. If the two drivers are 360 miles apart, how many hours will it be before they meet?

True or False: This is the correct equation to help us solve this problem: 65x+55x=360

• True

• False

Multiple Choice

Plane #1 and plane #2 are headed straight toward each other. Plane #1 is flying at 500 mph and plane #2 is flying at 575 mph. If the two planes are 5,375 miles apart, how many hours will it be before they meet?

True or False: This is the correct equation to help us solve this problem: 500x+575x=5,375

• True

• False

Multiple Choice

Runner #1 and runner #2 are headed straight toward each other. Runner #1 is traveling at 7 mph, and runner #2 is traveling at 10 mph. If the two runners are 34 miles apart, how many hours will it be before they meet?

Which equation will solve this problem?

• 7x+10x=34

• 34-7=10x

• 7+10+x=34

• 34x=7+10

Multiple Choice

Solve: Bird #1 and bird #2 are headed straight toward each other. Bird #1 is flying at 36 mph, and bird #2 is flying at 14 mph. If the two birds are 400 miles apart, how many hours will it be before they meet?

• 4 hours

• 5 hours

• 13 hours

• 8 hours