Question

question
solve for x and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution (∅), leave the number line blank.
-13 ≥ -4x - 9 and -21 ≥ -4x - 9
answer attempt 1 out of 2
inequality notation:
number line:
click and drag to plot line.
submit answer

Explanation:

Step1: Solve the first inequality \(-13 \geq -4x - 9\)

Add 9 to both sides: \(-13 + 9 \geq -4x - 9 + 9\)
Simplify: \(-4 \geq -4x\)
Divide both sides by -4 (and reverse the inequality sign): \(\frac{-4}{-4} \leq \frac{-4x}{-4}\)
Simplify: \(1 \leq x\) or \(x \geq 1\)

Step2: Solve the second inequality \(-21 \geq -4x - 9\)

Add 9 to both sides: \(-21 + 9 \geq -4x - 9 + 9\)
Simplify: \(-12 \geq -4x\)
Divide both sides by -4 (and reverse the inequality sign): \(\frac{-12}{-4} \leq \frac{-4x}{-4}\)
Simplify: \(3 \leq x\) or \(x \geq 3\)

Step3: Find the intersection of the two solutions

We have \(x \geq 1\) and \(x \geq 3\). The intersection of these two sets is \(x \geq 3\) (since all numbers greater than or equal to 3 are also greater than or equal to 1).

Answer:

Inequality Notation: \(x \geq 3\)

For the number line: Plot a closed circle at 3 and shade to the right.