Solve the inequality. Write the solution in set-builder notation.
Part B
Write an inequality for the problem. Let n = the number.
One eighth of a number is less than or equal to 3.
Solve the inequality. Write the solution in set-builder notation. Part B Write an inequality for the problem. Let n = the number. One eighth of a number is less than or equal to 3.
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To translate the problem into an inequality, we can express “one eighth of a number” mathematically as (frac{1}{8}n). The phrase “is less than or equal to” translates to the inequality sign (leq). Therefore, the inequality is:
[
frac{1}{8}n leq 3
]
Now, let’s solve this inequality for (n):
1. Multiply both sides by 8 to eliminate the fraction (note that since we are multiplying by a positive number, the direction of the inequality remains the same):
[
n leq 3 times 8
]
2. Calculate the right side:
[
n leq 24
]
Now, we can express the solution in set-builder notation. This indicates all values of (n) that satisfy the inequality:
[
{ n | n leq 24 }
]
So, the final solution in set-builder notation is:
[
{ n | n leq 24 }
]
If you need further assistance with inequalities or any other topics, feel free to ask!