Math 6H (Period 3)

Writing Equations 5.2

An equation is a mathematical sentence; a statement that uses an equal sign to separate two equal expressions     expression = expression

An equation has two sides à a left side and a right side!

For example    x + 5 = 7

A solution of an equation involving one variable is a value of the variable that makes the equation true.  For example 2 is a solution of x + 5 = 7 because  2 + 5 = 7  is a TRUE statement.

Finding all the solutions of an equation is called solving the equation.

Some equations are simple enough to solve using mental math.  We will use those simple equations to build our understanding of the algebraic method of solving equations.

A phrase does not usually contain a verb but a sentence MUST contain a verb. The verb in an equation is usually either “is”, equals”  or “is equal to”

We practiced translating several sentences into algebraic equations, such as:

The sum of a number and 8 is 17à n + 8 =17

Five less than a number is 9 à  x - 5 = 9

Fourteen equals 8 times a number à 14 = 8m

The quotient of 12 and a number is 4 à 12/y = 4

Sometimes it is a good idea to break down the verbal sentences when translating to an algebraic equation.  Circle the operation  and place the algebraic sign for that operation.  We wrote out our verbal sentences and below the “is” we wrote +. Then we took each part and translated it carefully.

Another method is the following  example:
The sum ( write +) of 3 ( write 3 before the +) and a number (write n after the +) is (write =) 10 ( write 10 after the =)

Explain why the equations x + 3 = 5 and 3 + x = 5 have the same solutions but the equations x – 3 = 5 and 3 – x = 5 do not.