Translate the following statement to an inequality. Then, find the solution.
Three times the sum of a number and five is greater than or equal to negative six.
n ≥ -7
n ≤ -7
n ≥ -3
n ≤ -3
3 (n + 5) >/= -6
3 n + 15 >/= -6
n + 5 >/= -2
n >/= -7
3(n + 5) ≥ -6
3n + 15 ≥ -6
3n ≥ -21
n ≥ -7
To translate the given statement to an inequality, let's break it down step-by-step:
1. Let's assume the number is represented by the variable n.
2. The sum of the number and five can be written as (n + 5).
3. Three times the sum of the number and five is represented by 3(n + 5).
4. The given statement says "Three times the sum of a number and five is greater than or equal to negative six", which can be written as 3(n + 5) ≥ -6.
Now, let's find the solution by solving the inequality:
3(n + 5) ≥ -6
3n + 15 ≥ -6
3n ≥ -6 - 15
3n ≥ -21
n ≥ -21/3
n ≥ -7
Therefore, the solution to the inequality is n ≥ -7.
To translate the statement to an inequality, let's break it down step by step:
Step 1: Identify the unknown number
The unknown number in this statement is represented by "n".
Step 2: Break down the given statement
"Three times the sum of a number and five" can be represented as "3(n + 5)".
Step 3: Translate "is greater than or equal to negative six"
This translates to "≥ -6".
Combining all the above steps, we can write the inequality as:
3(n + 5) ≥ -6
Now, let's solve the inequality to find the solution:
Step 1: Distribute 3 to both terms inside the parentheses:
3n + 15 ≥ -6
Step 2: Move 15 to the other side of the inequality by subtracting it from both sides:
3n ≥ -6 - 15
3n ≥ -21
Step 3: Divide both sides of the inequality by 3:
n ≥ -21/3
n ≥ -7
Therefore, the solution to the inequality is n ≥ -7.
So, the correct answer is n ≥ -7.