solving an equation with one unknown from arithmetic to algebra modifying equations in algebra

Solving an equation with one unknown

From arithmetic to algebraModifying equations in algebra


Today, we will use the rules of arithmetic seen last week to solve an equation with one unknownAs for last week, the exercises for next

week are intended to get you used to solving equations

Again, the slides provide list of properties you can go back to for reference


From arithmetic to algebra

Solving equations


Last week we saw the rules for using addition, subtraction, multiplication and division to perform calculationsLike the examples we’ve seen…

Today we examine how you can use the same rules and notation to solve equationsWhat’s the difference ?


An equation is a line of calculation that contains an “=” sign:

An equation can contain unknown “x, y, z” the value of which is not given

The numbers that are known are called parameters

2 4 6

2 6x


With the calculations, the aim was to find the following result (for example):

In fact, a calculation is simply an equation where the unknown is isolated on one side of the equation !!

2 46

5 2

2 46 ??

5 2


When an equation contains an unknown “x” the aim is to find the value(s) of “x” for which the equation is true In other words, “solving an equation” means

finding the value of the unknown for which the equality holds

Example : is the equation true if x=10? What if x=-20?

26 0

5 2

x


In the general case, the unknown is not isolated, like in a calculation:

Therefore, the aim is to modify the equation until you can isolate the unknown:

At that point, what you have is a calculation you can solve

4 6 5 2 2x

2 46

5 2x


The rules in the following section also apply to the case where the parameters of the equation (the numbers) are also unknown

However, you can use the same method to isolate the unknown It is simply the final calculation that you can’t

perform. You have some examples in the exercises

4 2x a b c



Solving equations

Solving equations

Lets try and solve the following equation In other words find the value of x such that

the equation is true.

The goal is to isolate “x” on one side. How do you do it? Use the rules from last week. Identify the grouped operations Move the groups until you have isolated x Important: take all the steps you need to do so !

4 6 5 2 2x

Solving equations

When modifying the equation take advantage of the fact that carrying out an operation on both sides of an equation does not change the equation

Step 1: move “2” to the other side

4 2 6 5 2 2 2x

4 6 5 2 2x

4 2 6 5 2 2 2x

4 2 6 5 2x

Solving equations

Step 2: if you want, you can carry out some calculations at the same time

Step 3: Move ×3 to the other side by dividing both sides by 3:

6 6 3x

4 2 6 5 2x

6 36

3 3x

2 6x

Solving equations

Step 4: Move -6 to the other side by adding 6 on both sides

Step 5: Perform the final calculation:

Step 6: ALWAYS check by replacing x in the original equation to see if it is true!!

2 6 x

2 6 6 6x

8 x

solving an equation with one unknown from arithmetic to algebra modifying equations in algebra

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