Let’s take a look at how to solve simple equations. These types of questions show up on the no-calculator part of the CAEC test. The goal is always the same: figure out what number x stands for.
We’ll use just one method, and it works every time. You don’t need to memorize anything fancy. The trick is this:
Whatever you do to one side of the equation, you must do the same thing to the other side.
That’s how we isolate x.
🔹 Example 1:
x − 8 = 9
To get x by itself, we do the opposite of subtracting 8.
Add 8 to both sides.
Left side: x − 8 + 8 = x
Right side: 9 + 8 = 17
Final Answer: x = 17
🔹 Example 2:
x ÷ 4 = 6
To undo division, we multiply both sides by 4.
Left side: (x ÷ 4) × 4 = x
Right side: 6 × 4 = 24
Final Answer: x = 24
🔹 Example 3:
2x = 150
To undo multiplication, we divide both sides by 2.
Left side: 2x ÷ 2 = x
Right side: 150 ÷ 2 = 75
Final Answer: x = 75
🔹 Example 4:
x − 100 = 225
Add 100 to both sides.
Left side: x − 100 + 100 = x
Right side: 225 + 100 = 325
Final Answer: x = 325
🔹 Example 5:
−271 − x = 873
We want to isolate x.
Step 1: Add 271 to both sides to cancel out the −271.
Left side: −271 + 271 − x = −x
Right side: 873 + 271 = 1144
Now we have: −x = 1144
Step 2: Multiply both sides by −1 to flip the sign.
Left side: −x × (−1) = x
Right side: 1144 × (−1) = −1144
Final Answer: x = −1144
Summary:
Just follow one method every time:
If something is subtracted, add it to both sides
If something is divided, multiply
If something is multiplied, divide
If you get −x, multiply both sides by −1
Keep both sides balanced, and you’ll get x by itself. Practice this method, and you’ll be ready for any equation on test day.