Answer:
M < 13
Step-by-step explanation:
Step 1: Look at the problem and what you're being asked to do.
Here, you have an inequality in one variable (to the first degree) with the variable on one side only. A number is added to the variable. You're asked to find possible values of the variable that make this inequality true.
(When we refer to "sides", we're talking about the "left side" being the expression to the left of the comparison symbol (<) and the "right side" being the expression to the right of the comparison symbol.)
Step 2: Identify the operations performed on the variable, and the order in which they are performed.
Here, only one operation is performed--the addition of -7.
Step 3: Do the operations that reverse the effects of the operations identified in step 2. Do these reverses starting from the last operation performed on the variable and working up the list to the first operation performed on the variable
Here, you want to "undo" the addition of -7. To do that, you add its opposite, +7 (to both sides of the inequality).
Now, you have ...
M - 7 + 7 < 6 + 7
Generally, you will collect terms or simplify the equation as a part of performing this "undo" operation. After simplification, the result is ...
M < 13
This is what the solution looks like, so you are done.
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Comment on the process
The process is the same for inequalities as for equations, with one exception. You need to pay attention to the ordering symbol when you use an operation that changes ordering.
Addition, subtraction, multiplication (or division) by a positive number do not change ordering. Multiplication or division by a negative number does change the ordering, so the symbol needs to be reversed in such cases.
Consider 2 > 1. When this is multiplied by -1, the > symbol needs to be changed to < as follows: -2 < -1.
Inviolable Rule: Whatever you do to one side of an equation (or inequality), you must also do to the other side.
