Practice: Two Step Equations

Practice: Two Step Equations

First things first

When you have a linear equation in one variable, a straightforward way to solve it is to "bring" all terms with the variable to the left, and all terms without it to the right.

​

But don't forget, when a term switches sides, it must also switch signs.​

For Example:

​​7x + 13 = 2x + 28

These terms are in the "wrong" places

​​7x + 13 = 2x + 28

So bring them to the opposite side

​​7x - 2x = -13 + 28

​

(But don't forget to switch their signs upon doing so)​

Simplify.

​​5x = 15

​

​

Divide both sides of the equation by the variable's coefficient.

Simplify again.

​​x = 3

​

​

When the equation looks like this:

9x - 14 = 40

​

It can be done in "two steps"

Preferably mentally.​

The same rules apply.

9x - 14 = 40

​

​

Step 1

9x = 40 + 14

​

​Bring that -14 to the right, and it becomes +14

Step 1

9x = 54

​

Simplify

Step 2

Step 2

x = 6

​

Simplify

x = 6

​

Solved

The process is so simple, you can do it mentally

2x + 17 = 3

​

Let's do that again

​

Step 1

2x = 3 - 17

​

(Try doing these steps purely in your mind)

​

Step 1

2x = -14

​

​

​

Step 2

Step 2

x = -7

​

Done!​

​

Speed Challenge​

Actually, more of a practice round

Fill in the Blanks

7x - 10 = 11

Fill in the Blanks

-4x + 13 = 53

Fill in the Blanks

5x - 17 = -22

Fill in the Blanks

-6x + 19 = -5

Fill in the Blanks

-3x - 14 = 4

Fill in the Blanks

2x - 6 = 4

Fill in the Blanks

11x + 13 = -31

Fill in the Blanks

-5x - 19 = -54

Fill in the Blanks

8x - 36 = 20

Fill in the Blanks

9x + 17 = -10

The End

As-salamu Alaykum