Question

solve for x and graph the solution on the number line below.
24 < -5x + 9 or -5x + 9 ≤ -1
answer attempt 1 out of 3
< > ≤ ≥ or
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
click and drag to plot line.
submit answer

Explanation:

Step1: Solve the first inequality \(24 < - 5x+9\)

Subtract 9 from both sides:
\(24 - 9 < -5x+9 - 9\)
\(15 < - 5x\)
Divide both sides by - 5 and reverse the inequality sign (since dividing by a negative number):
\(\frac{15}{-5}>x\)
\(x < - 3\)

Step2: Solve the second inequality \(-5x + 9\leq-1\)

Subtract 9 from both sides:
\(-5x+9 - 9\leq-1 - 9\)
\(-5x\leq-10\)
Divide both sides by - 5 and reverse the inequality sign:
\(\frac{-5x}{-5}\geq\frac{-10}{-5}\)
\(x\geq2\)

Answer:

Inequality Notation: \(x < - 3\) or \(x\geq2\)

To graph on the number - line:

• For \(x < - 3\), draw an open circle at \(x = - 3\) and shade to the left.
• For \(x\geq2\), draw a closed circle at \(x = 2\) and shade to the right.