What is the greatest integer value of k that satisfies the inequality 8 - 3(2k - 5) \geq 4… — ACT

What is the greatest integer value of $k$ that satisfies the inequality $8 - 3(2k - 5) \geq 4(k + 6)$ ?

Answer: -1

The greatest integer value of

k

that satisfies the inequality is

-1

Solving the inequality step-by-step yields

k \leq -0.1

. The greatest integer less than or equal to

-0.1

-1

Distribute the coefficients to remove parentheses

8 - 6k + 15 \geq 4k + 24

Expanding the terms makes it possible to combine like terms on each side of the inequality.

Combine like terms on the left side

23 - 6k \geq 4k + 24

Simplifying the constant values on the left side (

8 + 15 = 23

) simplifies the expression.

Subtract

4k

from both sides

23 - 10k \geq 24

This groups all the variable terms on the left-hand side.

Subtract

23

from both sides

-10k \geq 1

This isolates the variable term on the left-hand side.

Divide by

-10

and flip the inequality sign

k \leq -0.1

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

Identify the greatest integer satisfying the inequality

k = -1

The largest integer that is less than or equal to

-0.1

-1

Solving linear inequalities and applying the sign-flip rule when dividing by a negative number.

Estimated Time:1m 30s

Question