Question

solve for x and graph the solution on the number line below.
3 ≥ x - 7 > 1
answer attempt 1 out of 3
< > ≤ ≥ or
inequality notation:
number line:

Explanation:

Step1: Solve the left - hand side inequality

We have \(3\geq x - 7\). Add \(7\) to both sides of the inequality:
\(3+7\geq x-7 + 7\), which simplifies to \(10\geq x\) or \(x\leq10\).

Step2: Solve the right - hand side inequality

We have \(x - 7>1\). Add \(7\) to both sides of the inequality:
\(x-7 + 7>1+7\), which simplifies to \(x>8\).

Answer:

Inequality Notation: \(8 < x\leq10\)

To graph on the number line:

• Draw an open circle at \(x = 8\) (because \(x>8\), the value \(8\) is not included in the solution set).
• Draw a closed circle at \(x = 10\) (because \(x\leq10\), the value \(10\) is included in the solution set).
• Connect the two points with a line segment.