Question

linear inequality and number line (l2)
question
solve the inequality and graph the solution on the line provided.
-8 - 4x > -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 8 to both sides

To isolate the term with \( x \), we add 8 to both sides of the inequality \(-8 - 4x > -16\). This gives \(-8 - 4x + 8 > -16 + 8\), which simplifies to \(-4x > -8\).

Step2: Divide by -4 (reverse inequality)

When dividing both sides of an inequality by a negative number, we reverse the inequality sign. Dividing both sides of \(-4x > -8\) by \(-4\) gives \(x < 2\) (since \(\frac{-4x}{-4} < \frac{-8}{-4}\) simplifies to \(x < 2\)).

Answer:

Inequality Notation: \( x < 2 \)
For the number line: Plot an open circle at 2 (since the inequality is strict, \( x
eq 2 \)) and draw an arrow to the left (indicating all values less than 2).