What is the maximum value of x that satisfies the inequality \frac{2 - 5x}{3} \ge 2x + 8? — ACT

What is the maximum value of $x$ that satisfies the inequality $\frac{2 - 5x}{3} \ge 2x + 8$ ?

Answer: -2

-2

Solving the inequality by isolating

x

leads to

x \le -2

, meaning that any value of

x

less than or equal to

-2

satisfies the inequality. Therefore, the maximum possible value is

-2

Multiply both sides of the inequality by 3 to clear the denominator.

2 - 5x \ge 6x + 24

Multiplying by a positive number eliminates the fraction without changing the inequality direction.

Subtract

6x

from both sides of the inequality.

2 - 11x \ge 24

This gathers the variable terms on the left side of the inequality.

Subtract 2 from both sides of the inequality.

-11x \ge 22

This isolates the variable term on the left side.

Divide both sides by

-11

and reverse the inequality sign.

x \le -2

Dividing by a negative number requires reversing the direction of the inequality sign. The resulting inequality defines the upper bound for

x

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

Question