M < 13
Step-by-step explanation:
If you had the equation ...
... M - 7 = 6
you would know immediately that M = 13. You would know this based on number facts you learned in 2nd grade, where you solved problems that looked like ...
... ___ - 7 = 6
Now that you're taking algebra, we give a name to the blank (here, that name is M). And we formalize rules that help us solve such equations. The primary rule, which you must always observe, is "whatever you do to one side of the equation, you must also do to the other side."
In this instance, we invoke that rule to add 7 to both sides of the equation. (We choose to add 7 because it is the opposite of -7, the number that was added to M. We know that adding 7 to -7 will give 0.)
... M - 7 + 7 = 6 + 7 . . . . 7 added to both sides
... M + 0 = 13 . . . . . . . . . simplify
... M = 13 . . . . . . . . . . . . use the identity property of 0, which says M+0 = M. (This should be fairly intuitive—adding nothing leaves only the original.)
Your expression is an inequality. This means the equal sign has been replaced by a comparison symbol (less than, in this case). The rules of manipulating such expressions are still the same, with an exception.
We can add or subtract the same thing from both sides without worry. And we can multiply or divide both sides by positive numbers without worry.
However, when we multiply or divide (which we must do to both sides) by a negative number, the sense of the comparison is reversed (less than becomes greater than, and vice versa). You can see the logic of this if you just consider the relations ...
... 2 > 1
... -2 < -1 . . . . . . both sides multiplied (or divided) by -1
Back to the Problem At Hand
... M - 7 < 6
Add 7 to both sides. (The reason is explained above.)
... M < 13 . . . . . . . . . If you followed the simplification for the equation, it is the same here.
