Solve the compound inequality. Express the answer in interval notation.
(B) $2x-3\le 1$ or $-x+4\le 10$

• A. $(-\infty ,-14]\cup [-1,\infty )$
• B. $[-6,2]$
• C. $(-\infty ,-6]\cup [2,\infty )$
• D. $(-\infty ,\infty )$

Answer: (D)

Verified step by step guidance

1. Identify the two inequalities given in the compound inequality: \$2x - 3 \leq 1\( and \)-x + 4 \leq 10$.
2. Solve the first inequality \$2x - 3 \leq 1\( by isolating \)x\(: add 3 to both sides to get \)2x \leq 4\(, then divide both sides by 2 to find \)x \leq 2$.
3. Solve the second inequality \(-x + 4 \leq 10\) by isolating \(x\): subtract 4 from both sides to get \(-x \leq 6\), then multiply both sides by \(-1\) (remember to reverse the inequality sign) to get \(x \geq -6\).
4. Since the compound inequality uses "or", the solution is all values of \(x\) that satisfy either \(x \leq 2\) or \(x \geq -6\).
5. Combine the solution sets: \(x \leq 2\) includes all numbers less than or equal to 2, and \(x \geq -6\) includes all numbers greater than or equal to -6. Together, these cover all real numbers, so the solution in interval notation is \((-\infty, \infty)\).