<p>If \(a - 1 \leq 7\), then find the range of \(a\).</p>
Step-by-Step Solution
Key Concept: Apply inverse operations to isolate the variable: adding 1 to both sides of the inequality preserves the inequality sign since we're performing the same operation on both sides.
<p><strong>Step 1:</strong> Start with the given inequality: <em>a</em> − 1 ≤ 7</p><p><strong>Step 2:</strong> Add 1 to both sides (this does not change the inequality sign): <em>a</em> − 1 + 1 ≤ 7 + 1</p><p><strong>Step 3:</strong> Simplify: <em>a</em> ≤ 8</p><p><strong>Step 4:</strong> The range of <em>a</em> is all real numbers less than or equal to 8, written in interval notation as: <em>a</em> ∈ (−∞, 8]</p><p>∴ Answer: B (assuming B represents <em>a</em> ≤ 8 or (−∞, 8])</p>
Correct Answer: B