Question

linear inequality and number line (l2)
question
solve the inequality and graph the solution on the line provided.
-2x - 21 ≥ -35
the number of attempts on this specific problem before you are marked incorrect
answer
attempt 1 out of 2
< > ≤ ≥ 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: Add 21 to both sides

To isolate the term with \( x \), we add 21 to both sides of the inequality \( -2x - 21 \geq -35 \). This gives us \( -2x - 21 + 21 \geq -35 + 21 \), which simplifies to \( -2x \geq -14 \).

Step2: Divide by -2 (reverse inequality)

When dividing an inequality by a negative number, we reverse the inequality sign. Dividing both sides of \( -2x \geq -14 \) by -2, we get \( \frac{-2x}{-2} \leq \frac{-14}{-2} \), which simplifies to \( x \leq 7 \).

Answer:

Inequality Notation: \( x \leq 7 \)
For the number line: Plot a closed circle at 7 (since the inequality is "less than or equal to") and draw a line to the left of 7 to represent all values of \( x \) that satisfy \( x \leq 7 \).