Answer:
1.9(2.3n+6)+10.45 > 43.7 is n > 5
Explanation:
To solve the inequality 1.9(2.3n+6)+10.45 > 43.7, you need to isolate the variable 'n'. Here's it broken down step-by-step:
1. Distribute 1.9 to both terms inside the parentheses:
1.9 * 2.3n + 1.9 * 6 + 10.45 > 43.7
4.37n + 11.4 + 10.45 > 43.7
2. Combine like terms:
4.37n + 21.85 > 43.7
3. Subtract 21.85 from both sides of the inequality to isolate the variable:
4.37n > 43.7 - 21.85
4.37n > 21.85
4. Divide both sides of the inequality by 4.37 to solve for 'n':
n > 21.85 / 4.37
n > 5
Solution graphed: Since 'n' is greater than 5, you have to represent the solution on a number line by shading everything to the right of 5. This indicates that any value of 'n' greater than 5 will satisfy the inequality.
Here's a visual representation:
-∞ 5 ➔ (shade to the right)
So, the solution to the inequality 1.9(2.3n+6)+10.45 > 43.7 is n > 5.