Introduction to Algebra

• Mathematics
• Secondary Education
• Age 11,12

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INTRODUCTION TO ALGEBRA by Sir Keevan Maharaj

Understanding the Basics of Algebra

Solving:            + 2 = 6

In algebra,          is called our unknown variable, and is represented by a letter (e.g., x). There are also constants, which are the known values in our equations.

 

Using this information, we can say that the new equation is x + 2 = 6. Constants: +2, 6

Using Algebra - Solve for x

Solving simple equations - Method 1:

Example 1: x - 2 = 4

Steps we can take to solve x:

1. Work out what should be removed to get "x =".

2. Remove it by doing the opposite (adding vs subtracting)

3. Do that to both sides

Using Algebra - Solve for x

Example 1: x - 2 = 4

Step 1: To make x the subject, we want to remove "-2".

Step 2: The opposite of "-2" is "+2".

Step 3: Doing the opposite on both sides: x - 2 + 2 = 4 + 2

Step 4: Solving for x: x + 0 = 6

Therefore, x = 6.

Why do we add '+2' on both sides?

We add '+2' on both sides to "KEEP THE BALANCE".

                                                          Add +2 to left side               Add +2 to right side

                In Balance                          Out of Balance!                    In Balance Again!

Using Algebra - Solve for x

Solving simple equations - Method 2:

Example 2: x + 8 = 12

Steps we can take to solve x:

1. Determine what number we need to move to make x the subject.

2. Move the number to the opposite side, changing the sign of the value (- to + or + to -).

3. Solve for x using the new equation.

Using Algebra - Solve for x

Example 2: x + 8 = 12

Step 1: To make x the subject, we want to move '+ 8'.

Step 2: We move '+ 8' from the left to the right so it becomes '- 8'

Step 3: The new equation "x = 12 - 8", and we solve for x using this.

Therefore, x = 4.

Algebra - Solve for x

Example 3: x - 12 = 6

• We want to remove/move '-12'
• The opposite of '- 12' is '+ 12'
• x = 6 + 12 OR x - 12 + 12 = 6 + 12
• x = 18 OR x + 0 = 18
• Therefore, x = 18

LET'S PRACTICE

Using the lessonup.app website, first click the 'x' in the bottom right, then go to the sidebar where you see 'Enter code', press and enter the 6-digit code you see on the screen.

Find x.

x + 12 = 36

1. 20
2. 22
3. 24
4. 26

Find x.

x - 5 = 10

1. 5
2. 15
3. 2
4. 10

Find x.

x + 9 = 3

1. 12
2. 6
3. -6
4. -12

Find x.

x - 19 = 21

1. 2
2. 40
3. - 40
4. - 2

Find x.

x + 5 = 21 - 3

1. 11
2. 16
3. 18
4. 13

REFLECTIONS

• Did we enjoy today's class?
• What did we learn today? Anything new?
• What topic/topics did we use today that we had previously covered?

Find x.

x + 12 = 17

1. 5
2. 29
3. 17
4. - 5

Find x.

x + 2 = - 5

1. 3
2. 7
3. - 7
4. - 3

Find x.

x + 2 = 9 - 8

1. 1
2. - 3
3. 3
4. -1

Find x.

x - 10 = - 23 + 8

1. - 15
2. 5
3. - 5
4. 15