Question

solve for x and graph the solution on the number line below.
3 ≤ x - 5 and 6 ≥ x - 5
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 the first inequality

We have the inequality \(3 \leq x - 5\). To solve for \(x\), we add 5 to both sides of the inequality.

$$
LATEXBLOCK0
$$

Step2: Solve the second inequality

We have the inequality \(6\geq x - 5\). To solve for \(x\), we add 5 to both sides of the inequality.

$$
LATEXBLOCK1
$$

Step3: Combine the two inequalities

From Step 1, we have \(x\geq8\) and from Step 2, we have \(x\leq11\). Combining these two inequalities, we get \(8\leq x\leq11\).

Answer:

Inequality Notation: \(8\leq x\leq11\)
For the number line: We plot a closed circle at 8 and a closed circle at 11, and draw a line segment between them.