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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
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