Questions: Solve for x and graph the solution on the number line below. -5 ≤ -5 x

Solution Steps

We are given the inequality \(-5 \leq -5x\). To isolate \(x\), we divide both sides by -5. Remember that when dividing or multiplying an inequality by a negative number, we must reverse the inequality sign. So, we have \[ \frac{-5}{-5} \geq \frac{-5x}{-5} \]

Simplifying the inequality gives us \[ 1 \geq x \]

We can rewrite the inequality \(1 \geq x\) as \(x \leq 1\).

To graph the solution \(x \leq 1\) on the number line, we place a closed circle at 1 (since \(x\) can be equal to 1) and shade the region to the left of 1, representing all values less than or equal to 1.

Final Answer