Translate the following statement to an inequality. Then, find the solution.
Four times the sum of a number and eight is greater than or equal to negative four.
n ≥ -9
n ≤ -9
n ≥ -32
n ≤ -32
4 ( n + 8 ) ≥ - 4
4 ∙ n + 4 ∙ 8 ≥ - 4
4 n + 32 ≥ - 4
Subtract 32 to both sides
4 n + 32 - 32 ≥ - 4 - 32
4 n ≥ - 36
Divide both sides by 4
n ≥ - 36 / 4
n ≥ - 9
To translate the statement to an inequality, let's break it down.
The sum of a number and eight can be written as "n + 8."
Four times the sum of a number and eight is "4(n + 8)."
The phrase "greater than or equal to" can be translated to the symbol "≥."
Putting it all together, the inequality becomes: 4(n + 8) ≥ -4.
To find the solution, we can solve this inequality step by step.
First, distribute the 4 to the terms inside the parentheses: 4n + 32 ≥ -4.
Next, isolate the variable by subtracting 32 from both sides: 4n ≥ -4 - 32 => 4n ≥ -36.
Finally, divide both sides by 4: n ≥ -36/4 => n ≥ -9.
Therefore, the solution to the inequality is n ≥ -9.
So the correct answer is n ≥ -9.