Nine more than half the number n is no more than -8. Write an inequality and find n.
"Nine more than half the number n" ---> (1/2)n + 9
(1/2)n + 9 "is no more than -8" -----> (1/2)n + 9 ≤ -8
carry on.
Thank you!
The inequality can be represented as:
(1/2)n + 9 ≤ -8
To solve for n, we need to isolate n on one side of the inequality.
(1/2)n ≤ -8 - 9
(1/2)n ≤ -17
To get rid of the fraction, we can multiply both sides by 2:
2 * (1/2)n ≤ 2 * -17
n ≤ -34
Therefore, the value of n is less than or equal to -34.
To solve this problem, let's break it down step by step.
The first part of the problem states: "Nine more than half the number n." This can be expressed as the mathematical expression (1/2)n + 9.
The second part of the problem states: "is no more than -8." This can be expressed as the inequality (1/2)n + 9 ≤ -8.
To find the value of n, we need to isolate it on one side of the inequality.
Let's solve the inequality step by step:
(1/2)n + 9 ≤ -8
Subtract 9 from both sides:
(1/2)n ≤ -8 - 9
(1/2)n ≤ -17
Multiply both sides by 2 to remove the fraction:
2 * (1/2)n ≤ 2 * (-17)
n ≤ -34
Therefore, the value of n is any number less than or equal to -34.
So, the inequality is n ≤ -34.