Solve the inequality and graph the solution.

Question

3m–7>5

Answer 1

To solve the inequality \(3m - 7 > 5\), we'll start by isolating \(m\).

1. Add 7 to both sides: \[ 3m - 7 + 7 > 5 + 7 \] Simplifying gives: \[ 3m > 12 \]

2. Next, divide both sides by 3: \[ m > \frac{12}{3} \] Simplifying gives: \[ m > 4 \]

So, the solution to the inequality is: \[ m > 4 \]

Graphing the Solution

To graph the solution \(m > 4\):

• Draw a number line.
• Place a point above 4, indicating that 4 is not included (since it is a strict inequality).
• Shade to the right of 4 to indicate that all numbers greater than 4 are included in the solution.

This indicates that \(m\) can take any value greater than 4.

Here is a simple ASCII representation of the graph:

<---|---|---|---|---|---|---|---|---|---|--->
...  3   4   5   6   7   8   9   ...
          (-------->

In this representation, the parenthesis at 4 shows that it is not included in the solution and the arrow indicates that the solution continues to infinity to the right.