Question

solve for x and graph the solution on the number line below.
$1 \geq \frac{x}{3}$
answer attempt 1 out of 2
inequality notation:
number line:

Explanation:

Step1: Multiply both sides by 3

To solve the inequality \(1 \geq \frac{x}{3}\), we multiply both sides by 3 to isolate \(x\). Since 3 is a positive number, the direction of the inequality sign remains the same.

$$ 1 \times 3 \geq \frac{x}{3} \times 3 $$

Step2: Simplify both sides

Simplifying the left - hand side \(1\times3 = 3\) and the right - hand side \(\frac{x}{3}\times3=x\). So we get \(3\geq x\), which can also be written as \(x\leq3\).

Answer:

Inequality Notation: \(x\leq3\)

For the number line graph:

• We draw a number line.
• We place a closed circle at \(x = 3\) (because the inequality is "less than or equal to", so 3 is included in the solution set).
• Then we draw an arrow starting from the closed circle at 3 and pointing to the left (towards negative infinity) to represent all the numbers less than or equal to 3.