What is the maximum integer value of k that satisfies the inequality 8 - 5k > 28? — ACT

What is the maximum integer value of $k$ that satisfies the inequality $8 - 5k > 28$ ?

Answer: -5

The maximum integer value that satisfies the inequality is

-5

Subtracting 8 from both sides of the inequality

8 - 5k > 28

yields

-5k > 20

. Dividing both sides of the inequality by

-5

and reversing the inequality sign results in

k < -4

. The largest integer strictly less than

-4

-5

Subtract 8 from both sides of the inequality.

-5k > 20

To isolate the term with the variable on the left side of the inequality.

Divide both sides by

-5

and reverse the inequality sign.

k < -4

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

Determine the largest integer strictly less than

-4

-5

Because the inequality is strict (

<

), the value of

k

cannot be equal to

-4

. The greatest integer less than

-4

-5

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

Question