Solve the inequality. Graph the solution set.

Question

negative 4 x greater than or equals 20−4x≥20
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Part 1
The solution set is StartSet x | nothing EndSetx | enter your response here.

Answer 1

To solve the inequality \(-4x \geq 20\), we will isolate \(x\).

1. Divide both sides of the inequality by \(-4\). Remember that when you divide by a negative number, you must reverse the inequality sign:

\[ x \leq \frac{20}{-4} \]

2. Simplifying the right side gives:

\[ x \leq -5 \]

The solution set for the inequality is therefore:

\[ { x \mid x \leq -5 } \]

Graphing the Solution Set:

1. On a number line, you would put a solid dot (or circle) on \(-5\) to indicate that it is included in the solution (since the inequality is \(\leq\)).
2. Shade all the numbers to the left of \(-5\) to show that \(x\) can be any value less than or equal to \(-5\).

The final representation of the solution set is:

\({ x \mid x \leq -5 }\)