📐 Basic Algebra Academy

Learn algebra step by step!

OpenEducation Presents: Algebra Academy

Welcome to Algebra Academy!

Algebra is a branch of mathematics where letters and symbols represent unknown numbers.

What will you learn?

  • Variables and algebraic expressions
  • Simplifying expressions
  • Combining like terms
  • The distributive property
  • Solving equations
  • Solving inequalities

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1. Variables and Expressions

A variable is a letter that represents an unknown or changing number.

x = 5

In this example, the variable x represents the number 5.

Algebraic expressions

An expression is a mathematical phrase containing numbers, variables, and operations.

x + 3

If x = 5, then:

5 + 3 = 8

Multiplication notation

In algebra, multiplication is often written without the multiplication sign.

3 × x = 3x

Important vocabulary

  • Variable: A letter representing a number.
  • Coefficient: The number multiplying a variable.
  • Constant: A number without a variable.
  • Expression: Numbers and operations without an equals sign.
7x + 4

7 is the coefficient, x is the variable, and 4 is the constant.

2. Simplifying Expressions

Simplifying means rewriting an expression in its simplest equivalent form.

Example 1

3 + 4 + 2

Add the numbers together:

9

Example 2

2x + 3x

Since both terms contain x, add their coefficients:

2x + 3x
(2 + 3)x
5x

Example 3

4x + 3 + 2x + 5

Group the variable terms and constants:

4x + 2x + 3 + 5
6x + 8
Answer: 6x + 8

3. Combining Like Terms

Like terms are terms that have exactly the same variables raised to the same powers.

Like terms

3x and 7x

These can be combined because they both contain x.

Unlike terms

3x and 7y

These cannot be combined because their variables are different.

More examples

5x + 2x = 7x
8y - 3y = 5y
4x + 3y + 2x = 6x + 3y

Remember: You can only add or subtract the coefficients of like terms.

4. The Distributive Property

The distributive property allows you to multiply a number by everything inside parentheses.

a(b + c) = ab + ac

Example 1

3(x + 4)
Multiply 3 by x: 3x
Multiply 3 by 4: 12
Combine: 3x + 12
Answer: 3x + 12

Example 2: Negative numbers

-2(x - 5)
-2 × x = -2x
-2 × -5 = +10
Answer: -2x + 10

Be careful with negative signs!

5. Solving One-Step Equations

An equation states that two expressions are equal.

The goal is to find the value of the variable.

Example 1: Addition

x + 5 = 12

Subtract 5 from both sides:

x + 5 - 5 = 12 - 5
x = 7

Example 2: Subtraction

x - 4 = 10

Add 4 to both sides:

x = 14

Example 3: Multiplication

3x = 18

Divide both sides by 3:

x = 6

Example 4: Division

x / 4 = 5

Multiply both sides by 4:

x = 20

Important: Whatever operation you perform on one side, perform it on the other side too.

6. Solving Two-Step Equations

Two-step equations require two inverse operations to isolate the variable.

Example

3x + 5 = 20

Step 1: Subtract 5 from both sides.

3x + 5 - 5 = 20 - 5
3x = 15

Step 2: Divide both sides by 3.

3x / 3 = 15 / 3
x = 5

Another example

2x - 7 = 9
Add 7 to both sides: 2x = 16
Divide by 2: x = 8
Answer: x = 8

7. Inequalities

Inequalities compare two values that may not be equal.

The four main symbols

< means less than
> means greater than
≤ means less than or equal to
≥ means greater than or equal to

Example 1

x + 3 > 8

Subtract 3 from both sides:

x > 5

This means x can be any number greater than 5.

Important rule

When multiplying or dividing an inequality by a negative number, reverse the inequality sign.

-2x > 8

Divide both sides by -2 and reverse the sign:

x < -4

📝 Algebra Practice

Solve the randomly generated algebra problem.

Enter the value of x.

Click New Question to begin.



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