What is the greatest integer value of x that satisfies the inequality 3 - 2x > 10? — ACT

What is the greatest integer value of $x$ that satisfies the inequality $3 - 2x > 10$ ?

Answer: -4

The correct answer is

-4

Subtracting 3 from both sides of

3 - 2x > 10

gives

-2x > 7

. When dividing both sides by

-2

, the inequality sign must be flipped, yielding

x < -3.5

. The greatest integer less than

-3.5

-4

Subtract 3 from both sides of the inequality to isolate the variable term.

-2x > 7

Subtracting 3 from both sides keeps the inequality balanced while moving the constant term to the right side.

Divide both sides by

-2

and reverse the inequality sign.

x < -3.5

Dividing or multiplying an inequality by a negative number requires reversing the direction of the inequality sign to maintain a true statement.

Identify the greatest integer that satisfies the inequality.

-4

The integers that are strictly less than

-3.5

are

-4, -5, -6, \dots

. The largest (greatest) of these integers is

-4

Solving linear inequalities by applying the sign-reversal rule when dividing by a negative number and identifying integer boundary values.

Question