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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
𝑥
2
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
1
Algebra book, a Statistics book has 1
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
 Geometry
3
𝑝
2
150 + 𝑝
2. Write a linear expression that
represents the total number of pages
in all the books that were given out.
3
4 𝑝 + 400 + 6𝑝 + 3(2𝑝) + 9 𝑝 + 4(𝑝 + 150)
2
3. Write down a simplified form of the
expression in (a) above.
67
𝑝 + 2200
2
4. If the total number of pages in all
the books is 8900 write an equations to
represent this.
67
𝑝 + 2200 = 8900
2
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 28, 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 = 28
2𝑥 + 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