Mod 3 Topic 1 Review

Combining Like Terms

100

Combine the like terms

x + 2x =

3x

200

Combine the like terms

9m - 7m + 13 =

2m + 13

300

Combine the like terms

4a + 8b

4a + 8b

400

Combine the like terms

-5y + 2y + 0.5f + 3g =

-3y + 0.5f + 3g =

500

Combine the like terms

11s + 0.78s - w = 

11.78s - w

One-Step Equations

100

Solve for x.

x + 15 = 22

x = 7

200

Solve for x.

x + 2.7 = 4.3 

x = 1.6

300

Solve for x.

5x = 75

x = 15

400

Solve for x.

10x - 4x = 30

x = 5

500

Solve for x.

1/2 (x) = 12

x = 24

Linear Expressions

100

Is this expression linear? Why or why not?

3x² + 5

No, because the expression has an exponent greater than 1. 

200

Is this expression linear? Why or why not?

8xy

No, because it has more than 1 variable

300

Is this expression linear? Why or why not?

4y

Yes, because it is the product of a constant and a single variable raised to the first power.

400

Is this expression linear? Why or why not?

-1 + 3x - 10x + 1/2

Yes, because it is the product of a constant and a single variable raised to the first power.

500

Is this expression linear? Why or why not?

x³ + x + 7

No, because it contains two variables instead of one.

Writing Expressions and Equations

100

Write an algebraic expression

You give an 18% tip for a meal. What expression represents the total cost with tip?

Let m = the cost of the meal 

y is the total cost

y = m + 0.18m 

y = m(1 + 0.18)

y = 1.18m

200

Write an algebraic expression

A pair of shoes sells for 1/4 off. What expression represents the total cost after the discount?

Let s = the original cost of the shoes ; y = total cost

y= s -1/4s 

y= s(1 − 1/4 )

y =  3/4s

300

Write an algebraic expression

A store discounts a new bike by 35% . What expression represents the total cost?

Let b = the original price of the bike; y = total cost

y = b − 0.35b 

y = b(1 − 0.35)

y = 0.65b

400

Write an algebraic expression

Katie starts a limousine rental company. As part of her research, Katie discovers that she must charge a 7% sales tax to her customers in addition to her rental fees

Let r = the rental fee; y = total cost

y = r + 0.07r

y = 1.07r 

500

BONUS POINTS!!!

:) 

Vocabulary

100

Variable

In algebra, a variable is a letter or symbol used to represent an unknown quantity

200

Like terms

Like terms are parts of an algebraic expression that have the same variable raised to the same power.

300

Numeric Coefficient

A numeric coefficient is a number multiplied by a variable expression. 

For example, in the expression − 2x, the number − 2 is a numeric coefficient. I

400

Inverse Operation

The opposite operation.

500

linear expression

any expression in which each term is a constant.

any expression in which the term is a product of a constant and a single variable raised to the first power.