Question

solve for x and graph the solution on the number line below.
-20 ≤ -4x - 4 or -4x - 4 ≤ -44
answer attempt 1 out of 3
< > ≤ ≥ or
inequality notation:
number line:
click and drag to plot line.

Explanation:

Step1: Solve the first inequality

Add \(4\) to both sides of \(-20\leq - 4x-4\):
\(-20 + 4\leq-4x-4 + 4\), which simplifies to \(-16\leq - 4x\).
Divide both sides by \(-4\). When dividing by a negative number, the inequality sign flips: \(\frac{-16}{-4}\geq\frac{-4x}{-4}\), so \(x\leq4\).

Step2: Solve the second inequality

Add \(4\) to both sides of \(-4x - 4\leq-44\):
\(-4x-4 + 4\leq-44 + 4\), which simplifies to \(-4x\leq-40\).
Divide both sides by \(-4\). When dividing by a negative number, the inequality sign flips: \(\frac{-4x}{-4}\geq\frac{-40}{-4}\), so \(x\geq10\).

Answer:

Inequality Notation: \(x\leq4\) or \(x\geq10\)

For the number - line:

• Place a closed (filled) circle at \(x = 4\) and draw a line to the left (towards more negative numbers).
• Place a closed (filled) circle at \(x = 10\) and draw a line to the right (towards more positive numbers).