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Variables and Algebraic Expressions

Write and evaluate algebraic expressions using variables.

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Variables and Algebraic Expressions

What Is a Variable?

A variable is a letter (like xx, yy, or nn) that represents an unknown number.

Algebraic Expressions

An algebraic expression contains numbers, variables, and operations.

ExpressionMeaning
x+5x + 5A number plus 5
3x3x3 times a number
x2\frac{x}{2}A number divided by 2
x2−4x^2 - 4A number squared minus 4

Evaluating Expressions

Substitute the value of the variable and calculate.

Evaluate 3x+73x + 7 when x=4x = 4: 3(4)+7=12+7=193(4) + 7 = 12 + 7 = 19

Evaluate x2−2x+1x^2 - 2x + 1 when x=3x = 3: 32−2(3)+1=9−6+1=43^2 - 2(3) + 1 = 9 - 6 + 1 = 4

Combining Like Terms

Like terms have the same variable raised to the same power.

5x+3x=8x7y−2y=5y5x + 3x = 8x \qquad 7y - 2y = 5y 4x+3y+2x+y=6x+4y4x + 3y + 2x + y = 6x + 4y

The Distributive Property

a(b+c)=ab+aca(b + c) = ab + ac

3(x+4)=3x+123(x + 4) = 3x + 12 −2(3x−5)=−6x+10-2(3x - 5) = -6x + 10

Remember: When writing expressions, 5×x5 \times x is written as 5x5x (skip the multiplication sign).

Explain using:

⚠️ Common Mistakes: Variables and Algebraic Expressions

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🌍 Real-World Applications: Variables and Algebraic Expressions

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📝 Worked Example: Solving a Quadratic by Factoring

Problem:

Solve x2−5x+6=0x^2 - 5x + 6 = 0.

2Factor the quadratic
3Set each factor equal to zero
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Exponents and Order of Operations
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📌 Related Topics in Variables and Expressions

Exponents and Order of Operations

❓ Frequently Asked Questions

What is Variables and Algebraic Expressions?▾
Write and evaluate algebraic expressions using variables.
How can I study Variables and Algebraic Expressions effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Regular review and active practice are key to retention.
Is this Variables and Algebraic Expressions study guide free?▾
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What course covers Variables and Algebraic Expressions?▾
Variables and Algebraic Expressions is part of the Pre-Algebra course on Study Mondo, specifically in the Variables and Expressions section. You can explore the full course for more related topics and practice resources.