Final answer:
The inequality representing 'negative one third is greater than or equal to the product of negative two fifths and a number' is -1/3 ≥ (-2/5)y. To solve for y, we multiply both sides by -5/2, leading to the solution y ≤ 5/6, which means y must be less than or equal to five sixths.
Step-by-step explanation:
To write and solve the inequality that represents "negative one third is greater than or equal to the product of negative two fifths and a number", we first translate the statement into mathematical symbols. The phrase 'negative one third' can be written as -1/3, 'greater than or equal to' is represented by ≥, 'the product of' indicates multiplication, and 'negative two fifths and a number' can be expressed as (-2/5)y, where y is the variable representing the number in question.
Putting this together, we get the inequality:
-1/3 ≥ (-2/5)y
To solve for y, we need to isolate the variable on one side of the inequality.
Step 1: Multiply both sides by -5/2 to cancel out the coefficient of y.
-5/2 * (-1/3) ≥ y
Step 2: Simplify the left side of the inequality.
y ≤ 5/6
The final inequality y ≤ 5/6 tells us that the variable y must be less than or equal to five sixths for the original inequality to hold true.