How to Solve the Inequality -7m ≥ -6m - 6 Step-by-Step
Quick Answer
To solve the inequality -7m ≥ -6m - 6, first collect all terms involving m on one side. This results in m ≤ 6, meaning m can be any value less than or equal to 6.
Inequalities can be a bit tricky at first, but with a step-by-step approach, they become much easier to handle. Let's break down the inequality
-7m ≥ -6m - 6 and find out what it means for the variable m.
### Step 1: Move all terms involving m to one side
To begin with, we want to isolate the variable m. This means we need to get all the m's on one side of the inequality. We can do this by adding 7m to both sides:
-7m + 7m ≥ -6m - 6 + 7m
0 ≥ m - 6
Now, we have simplified the inequality to just involve m on one side.
### Step 2: Isolate m
The next step is to isolate m completely. We can do this by adding 6 to both sides of the inequality:
0 + 6 ≥ m - 6 + 6
6 ≥ m
This tells us that m must be less than or equal to 6.
### Step 3: Rewriting the inequality
We can rewrite our final result in a more standard form:
m ≤ 6
### Understanding the Solution
This means that any value of m that is less than or equal to 6 will satisfy the inequality. To better understand this, let’s consider a few examples:
- If m = 6, then -7(6) = -42 and -6(6) - 6 = -36, making -42 ≥ -36 true.
- If m = 0, then -7(0) = 0 and -6(0) - 6 = -6, making 0 ≥ -6 true.
- If m = 7, then -7(7) = -49 and -6(7) - 6 = -48, making -49 ≥ -48 false.
### Real-World Applications
Understanding inequalities is crucial, as they are used in various real-world scenarios such as budgeting, engineering, and even in data science for comparisons and constraints. For example, if you are budgeting your monthly expenses, knowing that your expenses should not exceed a certain amount can be framed as an inequality.
### Conclusion
In summary, solving inequalities like -7m ≥ -6m - 6 involves manipulating the inequality to isolate the variable. Remember, the key steps are to get all m's on one side, isolate m, and then understand the implications of your solution. If you ever feel stuck, just break it down like we did here, and you’ll find clarity in no time! Check the equations section for more examples and practice problems.
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