Final answer:
To solve the inequality -3 + 1/2 ≤ 1/2(-n + 14), isolate the variable n. Distribute 1/2, simplify, add and subtract, multiply and reverse the inequality to obtain the solution.
Step-by-step explanation:
To solve the inequality -3 + 1/2 ≤ 1/2(-n + 14), we need to isolate the variable n.
1. Distribute 1/2 to -n and 14: -3 + 1/2 ≤ 1/2(-n) + 1/2(14)
2. Simplify: -3 + 1/2 ≤ -1/2n + 7
3. Add 3 to both sides to remove the -3: 1/2 ≤ -1/2n + 10
4. Subtract 10 from both sides to isolate -1/2n: -9.5 ≤ -1/2n
5. Multiply both sides by -2 to get rid of the fraction and reverse the inequality: 19 ≥ n
The solution to the inequality is n is greater than or equal to 19 but less than 19.