Write and solve the inequality that represents negative one fifth is greater than or equal to the product of negative two thirds and a number.
negative two thirds is less than or equal to negative one fifth y where y is less than or equal to two fifteenths
negative two thirds is less than or equal to negative one fifth y where y is greater than or equal to negative three tenths
negative one fifth is greater than or equal to negative two thirds y where y is greater than or equal to three tenths
negative one fifth is less than negative two thirds y where y is less than or equal to negative two fifteenths
The correct inequality that represents the given statement is:
-2/3 * x ≤ -1/5
To solve for x, we can multiply both sides of the inequality by (-5/2), noting that multiplying by a negative number will flip the inequality sign.
(-5/2) * (-2/3) * x ≥ (-5/2) * (-1/5)
Multiply the fractions:
5/3 * x ≤ 1
Divide both sides of the inequality by 5/3 (or multiply by its reciprocal, 3/5):
(3/5) * (5/3) * x ≥ (3/5) * 1
x ≥ 3/5
Therefore, the solution to the inequality is x ≥ 3/5.