For what greatest integer value of y is the inequality 9 - 2y \geq 16 true? — ACT

For what greatest integer value of $y$ is the inequality $9 - 2y \geq 16$ true?

Answer: -4

The greatest integer value of

y

that satisfies the inequality is

-4

Subtracting 9 from both sides of

9 - 2y \geq 16

gives

-2y \geq 7

. Dividing both sides by

-2

and reversing the inequality sign yields

y \leq -3.5

. The greatest integer less than or equal to

-3.5

-4

Subtract 9 from both sides of the inequality.

-2y \geq 7

This isolates the term containing

y

on the left side.

Divide both sides of the inequality by

-2

and reverse the direction of the inequality sign.

y \leq -3.5

Dividing both sides of an inequality by a negative number requires reversing the direction of the inequality sign.

Identify the greatest integer that is less than or equal to

-3.5

-4

The value of

y

must be less than or equal to

-3.5

. The integers satisfying this condition are

-4, -5, -6, \dots

, and the greatest of these is

-4

Solving linear inequalities by isolating the variable and reversing the inequality sign when dividing by a negative number.

Question