Final answer:
To solve the inequality 7.2 > 0.9(n+8.6), distribute the 0.9 across the parentheses, subtract 7.74 from both sides, and finally divide by 0.9 resulting in n < -0.6 as the solution.
Step-by-step explanation:
To solve the inequality 7.2 > 0.9(n+8.6), follow these steps:
- First, we want to isolate the variable n on one side of the inequality. Start by distributing the 0.9 through the parentheses: 0.9 × n + 0.9 × 8.6.
- This simplifies to 7.2 > 0.9n + 7.74.
- Next, subtract 7.74 from both sides of the inequality: 7.2 - 7.74 > 0.9n.
- This gives you -0.54 > 0.9n.
- Now, divide both sides by 0.9 to solve for n: -0.54 / 0.9 > n.
- The inequality then becomes -0.6 > n, which means that n must be less than -0.6.
The solution to the inequality is n < -0.6.