2.5 Solving linear equations with one unknown


Discuss and discover


Gina’s Trattoria Ristorante has only round tables. Each table seats 5 people. Some tables are in the lounge and some are on the patio. There are 20 tables in the lounge and 8 tables on the patio.


(i) Working with a classmate, draw a diagram to show how to calculate the total number of people that can be seated.


(ii) Gina removes some tables from the lounge. Use a variable to represent the number of tables that remain.


(iii) Write an algebraic expression for the number of people the restaurant can now seat.


(iv) Compare your diagram and expression with those of another pair of classmates. If your diagrams and expressions are different, are both of them correct? How can you check?


Comparing mathematical expressions and equations Expression


Meaning


What is it? Result


Relation symbol Sides


Example


An expression is a mathematical phrase which combines numbers,


variables and operators to show the value of something.


Stands for a single numerical value.


Simplifi cation No


One sided 8x − 2 ( 4x + 14 )


Solving an equation means fi nding the value(s) of the variable(s) that makes the equation a true statement.


Variable(s) in linear equations Variables in a linear equation cannot have exponents (or powers) other than 1. A linear equation will not contain any of the following: x2


or x3 or ‘ x times y ’ or xy or ‘ x divided by y ’ or x


_ y or √


_ x


By the end of this section you should be able to: ● solve linear equations with one unknown variable


Equation An equation is a mathematical


statement to show two expressions are equal to each other.


Shows equality between two expressions.


Solution Yes, equal sign ( = )


Two sided, left and right 7x − 5 = 19


Section A Applying our skills


41


variable


2 Exploring patterns, expressions, equations and functions


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