Question

solve for $x$ and graph the solution on the number line below.
$20\geq 5x + 10$ or $65\leq 5x + 10$
answer attempt 1 out of 3
inequality notation:
number line:

Explanation:

Step1: Solve the first inequality \(20\geq5x + 10\)

Subtract \(10\) from both sides:
\(20-10\geq5x+10 - 10\)
\(10\geq5x\)
Divide both sides by \(5\):
\(\frac{10}{5}\geq\frac{5x}{5}\)
\(2\geq x\) or \(x\leq2\)

Step2: Solve the second inequality \(65\leq5x + 10\)

Subtract \(10\) from both sides:
\(65 - 10\leq5x+10-10\)
\(55\leq5x\)
Divide both sides by \(5\):
\(\frac{55}{5}\leq\frac{5x}{5}\)
\(11\leq x\) or \(x\geq11\)

Answer:

Inequality Notation: \(x\leq2\) or \(x\geq11\)

For the number - line:

• Draw a closed circle at \(x = 2\) (because the inequality is \(\leq\)) and shade to the left (towards the negative direction).
• Draw a closed circle at \(x = 11\) (because the inequality is \(\geq\)) and shade to the right (towards the positive direction).