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## Lesson Intro: Expressions with Variables

In this lesson, Juni Mathematics instructor **Kadyn** talks about **variables and variable expressions** - foundational concepts in pre-algebra. Variables are important to know for higher levels of math, and are even used similarly in other subjects like computer science!

Read Kadyn's Intro to Variable Expressions lesson first to understand what variables are and how to use them in expressions. Then, use what you've learned with Kadyn's **warmup questions** on this page to solidify your understanding, and practice solving basic arithmetic problems with different variables.

Once you've checked your answers, you can also keep practicing using variables with Variable Expressions Drills and Word Problems.

## Warmup Problems

### For Problems 1-3, simplify the following expressions.

#### Problem 1:

Practice working with variables for addition and subtraction.

- x + 3x
- x - (-7x)
- (3 + 2x) - (5x - 7)
- 4x + (2 - (-3x + 7) - 5 - 2x)
- -3x - 3 + (2x - (5 + 7x))

#### Problem 2:

Practice working with variables for multiplication and division.

- 6 ⋅ 2y
- 3y ⋅ 4
- 3 ⋅ (3y + 2)
- 5 - |3 - 6|) ⋅ 2y
- (2 + 1) ⋅ 4y ÷ 2

#### Problem 3:

Practice simplifying expressions with multiple variables.

- 2x + 3x - 5y + y
- 3y + 7x - (5y - 2x)
- y + 2x - 3z + 4y - 7x - 6z
- 4 ⋅ (2x + y - 8) - (7x + 3y - 17)
- (3x + 9y + 18) ÷ 3

#### Problem 4:

Evaluate the following expressions with the given value for x.

- 3x

where x = 5 - 7x - 4 ⋅ 5

where x = 3 - 2 - (3 - 4x)

where x = -1 - (5 - (5 ⋅ 3 - 10x)) ÷ 5

where x = 2 - (-4x + 6) - (2 ⋅ (-5x + 4))

where x = -2

#### Problem 5:

Evaluate the following expressions with the given values for x and y.

- 5x - 2y + 7

where x = -1, y = -5 - 3x
^{2}+ 3 ⋅ (7 - 2y)

where x = 3, y = 2 - y + (-2 ⋅ (3x - 2y)) + (7 - 2x)

where x = 4, y = -1

## Find Solutions Below

## Solutions

### Problem 1:

- 4x
- 8x
- 3 + 2x - 5x + 7 = -3x + 10
- 4x + 2 + 3x - 7 - 5 - 2x = -3x - 10
- -3x - 3 + 2x - 5 - 7x = -8x - 8

### Problem 2:

- 12y
- >12y
- 9y + 6
- (5 - 3) ⋅ 2y = 4y
- 12y ÷ 2 = 6y

### Problem 3:

- 5x - 4y
- 3y + 7x - 5y + 2x = 9x - 2y
- -5x - 6y - 9z
- (8x + 4y - 32) - (7x + 3y - 17) = x + y - 15
- x + 3y + 6

### Problem 4:

- 3 ⋅ 5 = 15
- 7 ⋅ 3 - 4⋅ 5 = 21 - 20 = 1
- 2 - 3 + 4x = -1 + 4 ⋅ -1 = -5
- (5 - 15 + 10x) ÷ 5 = (-10 + 10x) ÷ 5 = -2 + 2x = -2 + 2 ⋅ 2 = 2
- -4x + 6 - (-10x + 8) = -4x + 6 + 10x - 8 = 6x - 2 = 6 ⋅ (-2) - 2 = -14

### Problem 5:

- 5 ⋅ (-1) - 2 ⋅ (-5) + 7 = -5 + 10 + 7 = 12
- 3 ⋅ (3^2) + 3 ⋅ (7 - 2 ⋅ 2) = 3 ⋅ 9 + 3 ⋅ (3) = 27 + 9 = 36
- y + (-6x + 4y) + 7 - 2x = -8x +5y + 7 = -8 ⋅ 4 + 5 ⋅ (-1) + 7 = -32 - 5 + 7 = -30

## More Exercises on Variables

We hope you enjoyed Kadyn's Warmup Problems with Variable Expressions! This lesson falls under our Pre-Algebra A course curriculum. Continue practicing variables with drills and word problems below. Or, review key terms and concepts with Kadyn's Intro to Variable Expressions lesson.

- Intro to Variable Expressions: Definitions and Approaches
- Variable Expressions Drills
- Word Problems with Variable Expressions

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