Final answer:
The inequality described is (x + 9) / 4 ≥ -2, and to solve it, we multiply both sides by 4 and then subtract 9 from both sides, yielding x ≥ -17 as the solution.
Step-by-step explanation:
The question presented is about solving an inequality. To express the inequality based on the given statement, 'The sum of a number and 9, divided by 4, is greater than or equal to -2,' we first use a variable for the unknown number, let's call it x. The sum of this number and 9 can be written as x + 9. Dividing this sum by 4 gives us (x + 9) / 4. We set this expression to be greater than or equal to -2, resulting in the inequality (x + 9) / 4 ≥ -2.
To solve this inequality, we need to perform two steps:
- Multiply both sides of the inequality by 4 to eliminate the denominator. This gives us x + 9 ≥ -8.
- Subtract 9 from both sides to solve for x, leading to x ≥ -17.
The solution to the inequality is x is greater than or equal to -17. When solving this sort of problem, we must remember the rules for dealing with the signs of numbers during addition, subtraction, multiplication, and division.