To solve the inequality \(-5x - 6 > 9\), follow these steps:
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Add 6 to both sides: \[ -5x - 6 + 6 > 9 + 6 \] Simplifying gives: \[ -5x > 15 \]
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Divide both sides by -5. Remember that when you divide or multiply by a negative number, you must reverse the inequality sign: \[ x < \frac{15}{-5} \] Simplifying gives: \[ x < -3 \]
So the solution to the inequality is \(x < -3\).
Graphing the Inequality:
- Draw a number line.
- Locate the point \(-3\) on the number line.
- Since the inequality is \(x < -3\), draw an open circle at \(-3\) to indicate that \(-3\) is not included in the solution.
- Shade the line to the left of \(-3\) to represent all numbers less than \(-3\).
Here is a representation of the graph:
<---(----|----|----|----|----|----|----|----->
-5 -4 -3 -2 -1 0 1 2
(The open circle at \(-3\) indicates that \(-3\) is not included in the solution, and the shading extends leftward.)
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