Question

linear inequality and number line (l2)
question
solve the inequality and graph the solution on the line provided.
$-2 + 7x \leq -16$
answer
attempt 1 out of 2
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
click and drag to plot line.

Explanation:

Step1: Add 2 to both sides

To isolate the term with \( x \), we add 2 to both sides of the inequality \(-2 + 7x \leq -16\). This gives us \( -2 + 2 + 7x \leq -16 + 2 \), which simplifies to \( 7x \leq -14 \).

Step2: Divide by 7

Next, we divide both sides of the inequality \( 7x \leq -14 \) by 7. Since 7 is a positive number, the direction of the inequality sign remains the same. So, \( \frac{7x}{7} \leq \frac{-14}{7} \), which simplifies to \( x \leq -2 \).

Answer:

Inequality Notation: \( x \leq -2 \)
For the number line: We plot a closed circle at -2 (because the inequality is \( \leq \)) and draw a line to the left of -2 to represent all values of \( x \) that are less than or equal to -2.