Explanation:
remember, when transforming an equation (or even an inequality), whatever we do, we must do in both sides of the equation to keep it true. it is like a balance : when we take something away from one cup of bowl, we need to take away the same thing from the other to keep it in balance. the same for adding stuff.
to solve such an equation (to find the value of x for which this equation is actually true), there are many roads that lead to Rome ...
what they did here :
1. eliminate the "- 15x" on the right side by adding 15x to both sides
-12x + 6 = -15x - 3 | add 15x to both sides
-12x + 15x + 6 = -15x + 15x - 3
2. simplify both sides (kind of cleaning up). terms with the same base (constant or variable) are being combined based on their factors and signs :
-12x + 15x = 3x
-15x + 15x = 0
3x + 6 = -3
3. eliminate the "+ 6" on the left side by subtracting 6 from both sides
3x + 6 - 6 = -3 - 6
4. again we simplify
+6 - 6 = 0
-3 - 6 = -9
3x = -9
5. eliminate the factor 3 on the left side by dividing both sides by 3
3x/3 = -9/3
6. simplify
x = -3