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 2 𝑥+ 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 1 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 3 2 𝑝 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)+9 3 2 𝑝 +4(𝑝+150)

3. Write down a simplified form of the expression in (a) above

4. If the total number of pages in all the books is 8900 write an equations to represent this. 67 2 𝑝+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 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 =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