Question

solve for x and graph the solution on the number line below.
2x - 1 ≤ -21 or 1 < 2x - 1
answer attempt 1 out of 2
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
touch and drag to plot line.
submit answer

Explanation:

Step1: Solve \(2x - 1 \leq -21\)

Add 1 to both sides: \(2x - 1 + 1 \leq -21 + 1\) → \(2x \leq -20\)
Divide by 2: \(\frac{2x}{2} \leq \frac{-20}{2}\) → \(x \leq -10\)

Step2: Solve \(1 < 2x - 1\)

Add 1 to both sides: \(1 + 1 < 2x - 1 + 1\) → \(2 < 2x\)
Divide by 2: \(\frac{2}{2} < \frac{2x}{2}\) → \(1 < x\) (or \(x > 1\))

Step3: Combine solutions

Since it's "or", the solution is \(x \leq -10\) or \(x > 1\)

Answer:

Inequality Notation: \(x \leq -10\) or \(x > 1\)
(For the number line: Plot a closed circle at \(-10\) and shade left, and an open circle at \(1\) and shade right.)