Questions: Consider the following inequality. -4 x ≤ -36 Step 1 of 2 : Write the solution using interval notation.

Solution Steps

To solve the inequality \(-4x \leq -36\), we need to isolate \(x\). This involves dividing both sides of the inequality by \(-4\). Remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign. Once \(x\) is isolated, we can express the solution in interval notation.

We start with the given inequality:

\[ -4x \leq -36 \]

To solve for \(x\), we need to isolate \(x\) on one side of the inequality. We do this by dividing both sides of the inequality by \(-4\). Remember, when dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

\[ x \geq \frac{-36}{-4} \]

Simplifying the right side:

\[ x \geq 9 \]

The solution \(x \geq 9\) can be expressed in interval notation. Since \(x\) can be any number greater than or equal to 9, the interval notation is:

\[ [9, \infty) \]

Final Answer