Question

solve the inequality and graph the solution on the line provided.
-16 + 7x < -65
answer attempt 1 out of 2
inequality notation:
number line:
number line with -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 \(7x < -65 + 16\). Calculating the right - hand side, \(-65+16=-49\), so the inequality becomes \(7x < - 49\).

Step2: Divide both sides by 7

To solve for \(x\), we divide both sides of the inequality \(7x < - 49\) by 7. Since 7 is a positive number, the direction of the inequality sign remains the same. So we have \(\frac{7x}{7}<\frac{-49}{7}\), 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, \(x
eq - 7\)) and draw an arrow to the left of \(-7\) to represent all the numbers less than \(-7\).