Question

solve the inequality and graph the solution on the line provided.
-16 + 7x < -65
answer attempt 1 out of 5
< > ≤ ≥ or
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
touch and drag to plot line.
submit answer

Explanation:

Step1: Add 16 to both sides

To isolate the term with \( x \), we add 16 to both sides of the inequality \(-16 + 7x < -65\). This gives us \( -16 + 16 + 7x < -65 + 16 \), which simplifies to \( 7x < -49 \).

Step2: Divide by 7

Next, we divide both sides of the inequality \( 7x < -49 \) by 7. Since 7 is positive, the direction of the inequality sign remains the same. So, \( \frac{7x}{7} < \frac{-49}{7} \), which simplifies to \( x < -7 \).

Answer:

Inequality Notation: \( x < -7 \)
For the number line: We draw an open circle at -7 (because the inequality is strict, \( < \), not \( \leq \)) and shade the line to the left of -7 to represent all values of \( x \) that are less than -7.