## 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, practice below with Kadyn's **practice drills** to solidify your understanding and challenge yourself to apply what you've learned.

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

## Warmup Problems

For Problems 1-4, simplify the following expressions.

### Problem 1:

Practice using variables with addition/subtraction.

- x + 2x
- 4x - 7x
- -3x + 5x
- (5 + 7x) - (3x - 4)
- 2x + 7 - (6 + x) + (-1 - 8x)

### Problem 2:

Practice simplifying expressions with multiple variables.

- 2y + 3x - 7y - 6x
- (3x + 3y) + y - 7 + 2x - 5y
- 5 - (x + x
^{2}-7) + 6x - 3x^{2} - (8 - x + 3y) - (|-8 +6| - 7x - y)
- (-3y - 4x + |2 - 9|) + (-2x + 9y)

### Problem 3:

Practice simplifying expressions with multiplication/division.

- (3y + 4) ⋅ 5
- 5 ⋅ (2 - (3y - 3))
- 3y + 2 ⋅ 7 - (-3 ⋅ 6y)) 7
- (3 ⋅ (7y - 2y) + 2 ⋅ 4 - |3 - 11|) 5y
- 9 + (3y + 2 ⋅ (2y - 3)) - (8 ⋅ (2 + 3y) 4)

### Problem 4:

Practice simplifying multi-step expressions with multiple variables.

- 4 - 6y 3 + 2x ⋅ 8
- 12x - 6y + (3 ⋅ 4x + 4 ⋅ 9) 6
- 2 ⋅ (4y + 3x - 9) - 4 ⋅ (3y +3x + 6)
- |3 - 9| ⋅ (-4x + 2y + 1) (-3)
- (15x
^{2}- |-3 - 6| + x + 3 ⋅ (3x + 3)) (-5)

### Problem 5:

Evaluate the following expressions with the given value for x.

- 7x - 3 ⋅ 4

where x = 2 - 3x
^{2}+ (-7x + 4x) - |3 - 9|

where x = 3 - 2 ⋅ (3x - 7) + (16x - 24)

where x = 5 - |-2| ⋅ (x
^{2}- 8x + 7) - (x^{2}+ 5x - 3)

where x = -2

### Problem 6:

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

- 2y - 7x + 5

where x = 3, y = -6 - 3x
^{2}- 8x - (-3y^{2}+ 5y + |3 + 4|)

where x = -2, y = 3 - (3 ⋅ (2x + 4y) - |7 - 13|) (-3)

where x = -5, y = 4

### Problem 7: Word Problem

Andrea has a son named Brock. In five years, Andrea will be 3 years older than six times Brock’s current age. If Brock is 6 years old now, what is Andrea’s current age?

### Problem 8: Word Problem

Marco challenges you to figure out his favorite number. He says if you multiply the number by -4, subtract 8, and divide it by 4, you will get 5. What is Marco’s favorite number?

## Find Solutions Below

## Solutions

### Problem 1:

- 3x
- -3x
- 2x
- 4x + 9
- -7x

### Problem 2:

- -3x - 5y
- -x -7y - 7
- -4x
^{2}+ 5x + 5 - 6x + 4y + 6
- 2x + 11y - 7

### Problem 3:

- 15y + 20
- 5 ⋅ (-3y + 5) = -15y + 25
- (21y + 14) 7 = 3y + 2
- (3 ⋅ 5y + 8 -8) 5y = 3
- 9 + (3y + 4y -6) - ((16 + 24y) 4) = 9 + (7y - 6) - (4 + 6y) = y - 1

### Problem 4:

- 4 - 2y + 16x
- 12x - 6y + (12x + 36) 6 = 12x - 6y + (2x + 6) = 14x - 6y + 6
- (8y + 6x - 18) - (12y + 12x + 24) = -6x - 4y - 42
- 6 ⋅ (-4x + 2y + 1) 3 = -8x + 4y + 2
- (15x
^{2}- 9 + x + 9x + 9) (-5) = (15x^{2}+ 10x) (-5) = -3x^{2}- 2x

### Problem 5:

- 7 ⋅ 2 - 3 ⋅ 4 - 14 - 12 = 2
- 3 ⋅ 9 + (-21 + 12) - 6 = 27 - 9 - 6 = 12
- 6x - 14 + 2x - 3 = 8x - 17 = 8 ⋅ 5 - 17 = 40 - 17 = 23
- (2x
^{2}- 16x + 14) - (x^{2}+ 5x -3) = x^{2}- 21x + 17 = 4 + 42 + 17 = 63

### Problem 6:

- 2 ⋅ -6 - 7 ⋅ 3 + 5 = -12 - 14 + 5 = -21
- 3 ⋅ (-2)
^{2}- 8 ⋅ (-2) - (-3 ⋅ (3)^{2}+ 5 ⋅ 3 + 7) = 12 + 16 - (-27 + 15 + 7) = 28 - (-5) = 33 - (6x + 12y - 6) (-3) = -3x - 4y + 2 = -3 ⋅ (-5) - 4 ⋅ 4 + 2 = 15 - 16 + 2 = 1

### Problem 7:

Andrea is currently 34 years old.

If Brock is 6 years old now, then in five years, Andrea will be 3 + 6 ⋅ 6 = 39 years old. Then currently, Andrea is 39 - 5 = 34 years old.

### Problem 8:

Marco’s favorite number is -7.

Let Marco’s favorite number be m. Then (-4 ⋅ m - 8) 4 = -m - 2 = 5. Then by guessing and checking, we know that m = -7.

## 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 variable expressions with warmup questions 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
- Warmup Problems with Variable Expressions
- Word Problems with Variable Expressions

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