Match the innequality to its graph.
6m + 5 > 9m - 4
To find the graph of the inequality 6m + 5 > 9m - 4, we need to solve it for m first.
First, we'll isolate the variable m by subtracting 6m from both sides:
5 > 3m - 4
Next, we'll isolate the variable m by adding 4 to both sides:
9 > 3m
Finally, we'll solve for m by dividing both sides by 3:
3 > m
Now we have the solution m < 3.
The graph of m < 3 will be a number line with an open circle at 3, indicating that 3 is not included in the solutions, and an arrow pointing to the left of 3, representing all values less than 3.
To solve the inequality 6m + 5 > 9m - 4, we can start by isolating the variable m on one side of the inequality.
First, let's subtract 6m from both sides:
6m + 5 - 6m > 9m - 4 - 6m
Simplifying the equation:
5 > 3m - 4
Next, let's add 4 to both sides:
5 + 4 > 3m - 4 + 4
Simplifying the equation:
9 > 3m
Finally, let's divide both sides by 3:
9/3 > 3m/3
Simplifying the equation:
3 > m
Now, we can represent the inequality graphically.
The inequality 6m + 5 > 9m - 4 can be represented by a graph where the solution set is all the values of m that are to the left of the vertical line which represents the point where m = 3.
The graph would look something like this:
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------------|------------> m
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The line indicates that the value of m is less than 3, which satisfies the inequality 6m + 5 > 9m - 4.
To determine the graph of the inequality 6m + 5 > 9m - 4, we need to solve it first.
Step 1: Start by getting all the m terms on one side of the inequality. Let's subtract 6m from both sides to isolate the m terms:
6m - 6m + 5 > 9m - 6m - 4
5 > 3m - 4
Step 2: Now, isolate the constant term on the other side of the inequality. Add 4 to both sides:
5 + 4 > 3m - 4 + 4
9 > 3m
Step 3: Finally, divide both sides by 3 to solve for m:
9/3 > 3m/3
3 > m
So, the inequality 6m + 5 > 9m - 4 is equivalent to m < 3.
For the graph of m < 3, you need to shade the region on a number line to the left of 3. The endpoint at 3 itself is not included in the solution.