Solve the inequality. Graph and check your solution.

Question

StartFraction x Over 5 EndFraction greater than minus 3
Question content area bottom
Part 1
x
▼
greater than
less than or equals
greater than or equals
less than
  
enter your response here ​(Simplify your​ answer.)

Answer 1

To solve the inequality \(\frac{x}{5} > -3\), we will first isolate \(x\).

1. Multiply both sides by 5 to eliminate the fraction. Since 5 is positive, the direction of the inequality will remain the same: \[ x > -3 \times 5 \] \[ x > -15 \]

Now that we have solved the inequality, we can summarize the solution:

\[ x > -15 \]

Graphing the Solution

To graph the inequality \(x > -15\), you can use a number line:

1. Draw a horizontal line and mark a point at \(-15\).
2. Since the inequality is strict (\(>\)), use an open circle at \(-15\).
3. Shade the region to the right of \(-15\), indicating all numbers greater than \(-15\).

Checking the Solution

To check if the solution is correct, you can substitute a number greater than \(-15\) into the original inequality. For example, let's use \(x = -10\):

\[ \frac{-10}{5} > -3 \] \[ -2 > -3 \quad \text{(True)} \]

Now, let's check a number that is not in the solution set (less than \(-15\)), such as \(x = -20\):

\[ \frac{-20}{5} > -3 \] \[ -4 > -3 \quad \text{(False)} \]

Thus, the solution \(x > -15\) is confirmed to be correct.

Final Answer

• The inequality is:

\[ x > -15 \]

• For your response box, select "greater than".