Question

question solve for x and graph the solution on the number line below.
-1 ≤ (\frac{x}{4})

Explanation:

Step1: Multiply both sides by 4

To solve for \( x \), we multiply both sides of the inequality \( -1 \leq \frac{x}{4} \) by 4. This is because we want to isolate \( x \), and multiplying both sides by the denominator (which is positive, so the inequality sign remains the same) will help us do that.
\[
4\times(-1) \leq 4\times\frac{x}{4}
\]

Step2: Simplify both sides

Simplifying the left side gives \( -4 \), and simplifying the right side (the 4s cancel out) gives \( x \). So we have:
\[
-4 \leq x
\]
Which can also be written as \( x \geq -4 \).

To graph this on a number line:

1. Draw a number line.
2. Locate the point -4.
3. Since the inequality is \( x \geq -4 \), we use a closed circle at -4 (because -4 is included in the solution set) and draw an arrow to the right (indicating all numbers greater than or equal to -4).

Answer:

The solution for \( x \) is \( x \geq -4 \). The graph has a closed circle at -4 and an arrow pointing to the right on the number line.