What You Will Learn
- Understand variables, constants, coefficients and terms.
- Write and interpret simple algebraic expressions.
- Collect like terms and simplify expressions.
- Use the distributive property correctly.
- Solve simple linear equations.
- Apply algebra to everyday mathematical problems.
What Is Algebra?
Algebra is a branch of mathematics that uses letters, numbers and symbols to represent quantities and relationships. A letter used to represent a number is called a variable.
Here, x is the variable and 7 is a constant.
Algebra helps us describe patterns and solve problems when a value is unknown.
Variables, Constants and Coefficients
Algebraic expressions are made from different parts. Understanding these parts makes it easier to read and simplify expressions.
5 is the coefficient, x is the variable, and 8 is the constant.
Terms and Expressions
A term is a number, a variable, or a product of numbers and variables. An algebraic expression is made up of one or more terms.
A single term.
A binomial expression.
A trinomial expression.
Writing Algebraic Expressions
Words can be translated into algebraic expressions. Look carefully at the operation described in the question.
Like Terms
Like terms contain the same variable raised to the same power. Only like terms can be combined by addition or subtraction.
Both terms contain x, so their coefficients can be added.
Combine the like terms 7a and −2a, while the constant 4 remains unchanged.
Using the Distributive Property
The distributive property allows a number outside brackets to multiply every term inside the brackets.
Multiply 3 by both x and 4.
Simplifying Algebraic Expressions
To simplify an expression, remove brackets when necessary and combine like terms.
Collect the like terms:
Then simplify:
Solving Simple Equations
An equation contains an equals sign. The goal is to find the value of the unknown variable. Keep the equation balanced by performing the same operation on both sides.
Subtract 5 from both sides:
Divide both sides by 3:
Equations with Two Steps
Some equations require more than one operation. Work backwards from the order of operations, undoing the operations one at a time.
First subtract 3:
Then divide by 2:
Algebra in Everyday Problems
Algebra can turn a word problem into an equation that can be solved.
A notebook costs ₦500. You have ₦2,000 and want to buy the same number of notebooks. Let x be the number of notebooks.
Divide both sides by 500:
Common Mistakes
Do not treat 3x and 4 as like terms. They have different forms.
Remember that x means 1x.
When distributing, multiply the outside factor by every term inside.
In an equation, perform the same operation on both sides.
Quick Practice
Try these questions before opening the answers.
- Simplify: 3x + 5x.
- Simplify: 7a − 2a + 3.
- Expand: 4(x + 2).
- Solve: x + 9 = 15.
- Solve: 3x = 21.
- Solve: 2x + 4 = 14.
Show answers
- 8x
- 5a + 3
- 4x + 8
- x = 6
- x = 7
- x = 5
Lesson Summary
- A variable represents an unknown or changing number.
- A constant is a fixed number.
- A coefficient multiplies a variable.
- Like terms can be combined.
- The distributive property removes brackets.
- Equations are solved by keeping both sides balanced.