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.

4x + 1 < -19 or 4x + 1 ≥ -11

answer attempt 1 out of 2

inequality notation:

number line:
number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12 marked

Explanation:

Step1: Solve \(4x + 1 < -19\)

Subtract 1 from both sides: \(4x + 1 - 1 < -19 - 1\)
Simplify: \(4x < -20\)
Divide both sides by 4: \(\frac{4x}{4} < \frac{-20}{4}\)
Simplify: \(x < -5\)

Step2: Solve \(4x + 1 \geq -11\)

Subtract 1 from both sides: \(4x + 1 - 1 \geq -11 - 1\)
Simplify: \(4x \geq -12\)
Divide both sides by 4: \(\frac{4x}{4} \geq \frac{-12}{4}\)
Simplify: \(x \geq -3\)

Step3: Combine the solutions (since it's "or")

The solution is \(x < -5\) or \(x \geq -3\)

Answer:

Inequality Notation: \(x < -5\) or \(x \geq -3\)

For the number line:

• For \(x < -5\), draw an open circle at \(-5\) and shade to the left.
• For \(x \geq -3\), draw a closed circle at \(-3\) and shade to the right.