Question

Solve 6(n)-3)-4|n| +5≤11.

Answer 1

To solve the inequality 6(n-3)-4|n| + 5 ≤ 11, we need to isolate the variable n and consider two cases: n ≥ 0 and n < 0.

Step-by-step explanation:

To solve the inequality 6(n-3)-4|n| + 5 ≤ 11, we need to isolate the variable n. Here is the step-by-step solution:

1. Distribute the 6: 6n - 18 - 4|n| + 5 ≤ 11
2. Combine like terms: 6n - 4|n| - 13 ≤ 11
3. Move all terms except the absolute value expression to the right side: 6n - 4|n| ≤ 24
4. Split the inequality into two cases:

• Case 1: n ≥ 0
• If n is greater than or equal to 0, the absolute value expression is equal to n: 6n - 4n - 13 ≤ 24
• Combine like terms: 2n - 13 ≤ 24
• Add 13 to both sides: 2n ≤ 37
• Divide by 2: n ≤ 18.5

• Case 2: n < 0
• If n is less than 0, the absolute value expression is equal to -n: 6n - 4(-n) - 13 ≤ 24
• Combine like terms: 10n - 13 ≤ 24
• Add 13 to both sides: 10n ≤ 37
• Divide by 10: n ≤ 3.7

Therefore, the solution to the inequality is n ≤ 18.5 when n is greater than or equal to 0, and n ≤ 3.7 when n is less than 0.