DAY 1 LINEAR EQUATIONS IN

ONE VARIABLE

INTRODUCTION.

Linear equations are encountered when dealing

with a number of real-life problems such as

distance problems, pricing problems, age problems

and finding dimensions of plane figures.

For instance, given the perimeter of a rectangular

piece of land and a brief description of its

dimensions, we can easily find the exact

dimensions using linear equations.

Examples of linear equations include:

3𝑦 = 6, 4𝑥 − 1 = 21 and 1

2𝑥 +

3

5= 5

We are going to learn how to form and solve linear

equations in one variable from word problems.

VOCABULARY

Variable : A symbol for a value that may change

depending on the conditions of a mathematical

problem.

Equation: Is a mathematical statement where

two expressions are equated.

A linear equation is an equation where the

variable in all the terms is raised to a power of

one.

CREATING A LINEAR EQUATION IN ONE

VARIABLE.

IN ORDER TO SOLVE A SIMPLE LINEAR

EQUATION FROM A WORD PROBLEM:

We read the problem carefully, noting what is

given and what is required.

We denote the unknown quantities or values by

the variables such as x or any other letter.

We change the problem to a mathematical

statement.

We form the linear equation in one variable using

the conditions given in the problem.

We then solve the equation for the unknown.

Lastly, we verify to be sure whether the answer

satisfies the conditions of the problem.

A teacher distributes different

mathematics books to students for their

study and revision. She gave out similar

copies of out 4 Trigonometry, 6 Algebra, 3

Pre-calculus, 9 Statistics and 4 Geometry

books. A Trigonometry book has 400 more

pages than an Algebra book, a Pre-calculus

book has twice the number of pages as an

Algebra book, a Statistics book has 11

2

times the number of pages as an Algebra

book and a Geometry book has 150 more

pages than an Algebra book.

1. Letting 𝑝 to represent the number

of pages in an Algebra book, write the

number of pages of each of the

trigonometry, algebra, pre-calculus,

and statistics and geometry book in

terms of 𝑝.

Trigonometry 400 + 𝑝

Algebra 𝑝

Pre-calculus 2𝑝

Statistics 3

2𝑝

Geometry 150 + 𝑝

2. Write a linear expression that

represents the total number of pages

in all the books that were given out.

4 𝑝 + 400 + 6𝑝 + 3(2𝑝) + 93

2𝑝 + 4(𝑝 + 150)

3. Write down a simplified form of the

expression in (a) above.

67

2𝑝 + 2200

4. If the total number of pages in all

the books is 8900 write an equations to

represent this.

67

2𝑝 + 2200 = 8900

5. Find the value of 𝑝.

200

6. Find the number of pages in an

algebra book.

200

7. Find the number of pages in the

other books

Trigonometry book: 600 pages

Pre−Calculus book: 400 pages

Statistics book: 300 pages

Geometry book: 350 pages

EXAMPLE 1

When two numbers are added, their sum is 28. If

one of the numbers exceeds the other by 8, find the

numbers.

SOLUTION

Let one of the numbers be x

Therefore, the other number = 𝑥 + 8

Their sum is 28, hence,

𝑥 + 𝑥 + 8 = 282𝑥 + 8 = 28

Subtracting 8 from both sides, we have,

HOMEWORK

A rectangle is such that its length is three times

its width. If it’s perimeter is 40 in, find the

dimensions of the rectangle.

ANSWERS TO HOMEWORK

The length of the rectangle is 15 in and the

breadth is 5 in.

THE END