Introduction to Algebra: Expressions, and Equations

Welcome to today’s math tutorial by AllCBTs!
In this lesson, we’re breaking down the core ideas in Algebra — a key concept in secondary school Mathematics, especially for WAEC, NECO, JAMB, and BECE candidates. Grab your writing materials and calculators — let’s begin!

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You can watch the full class in the video below:

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What Is Algebra?

Algebra is a broad and foundational area of mathematics that deals with:

• Expressions
• Equations
• Inequalities
• Quadratic equations

These tools are essential for solving real-world mathematical problems and are common in both junior and senior secondary syllabi.

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Algebraic Expressions

What Are Expressions?

Algebraic expressions involve:

• Variables (like x, y)
• Constants (like 2, 3)
• Mathematical operations (such as +, −, ×, ÷)

Examples of Expressions:

• 2x+32x + 32x+3
• x2−4x^2 – 4×2−4
• 3(x−2)3(x – 2)3(x−2)

Expressions are simply combinations of numbers, variables, and operations that do not contain an equals sign.

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Algebraic Equations

What Are Equations?

Equations occur when two algebraic expressions are equal to each other or to a number.
Equations help us to find the value of unknown variables.

Examples:

• 2x+3=52x + 3 = 52x+3=5
• x2−4=0x^2 – 4 = 0x2−4=0
• x+2=7x + 2 = 7x+2=7

Each equation can be solved to find the value of the variable that makes both sides equal.

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Inequalities

What Are Inequalities?

Inequalities compare two expressions using the following operators:

• Greater than >>>
• Less than <<<
• Greater than or equal to ≥\geq≥
• Less than or equal to ≤\leq≤

Examples:

• 2x+3>52x + 3 > 52x+3>5
• x2−4≤0x^2 – 4 \leq 0x2−4≤0
• x+2<7x + 2 < 7x+2<7

These symbols indicate ranges of values rather than single answers.

Understanding the Symbols:

• x>7x > 7x>7: x is greater than 7 → x could be 8, 9, 10, etc.
• x<6x < 6x<6: x is less than 6 → x could be 5, 4, 3, etc.
• x≤5x \leq 5x≤5: x is less than or equal to 5 → x could be 5, 4, 3…
• x≥6x \geq 6x≥6: x is greater than or equal to 6 → x could be 6, 7, 8…

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Quadratic Equations

What Are Quadratic Equations?

A quadratic equation is an equation where the highest power of the variable is 2.

General Form:

ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0

Where:

• aaa, bbb, and ccc are constants
• xxx is the variable

Quadratic equations appear frequently in senior secondary school and are vital for exam success.

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Watch more educational videos and past questions: https://youtube.com/@allcbts

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Final Takeaway

This lesson has introduced you to:

• The basics of algebra
• How to identify and solve expressions, equations, and inequalities
• A preview of quadratic equations and their form

With practice and good understanding, you’ll be able to tackle any algebraic problem confidently.

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Keywords

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