What is the smallest integer value of x that satisfies the inequality 11 - 3x < 2? — ACT

What is the smallest integer value of $x$ that satisfies the inequality $11 - 3x < 2$ ?

Answer: 4

The smallest integer value of

x

that satisfies the inequality is 4.

Solving the inequality

11 - 3x < 2

leads to

-3x < -9

. Dividing by

-3

and reversing the inequality sign gives

x > 3

. The smallest integer that is strictly greater than 3 is 4.

Isolate the variable term on one side of the inequality by subtracting 11 from both sides.

-3x < -9

Subtracting 11 from both sides of the inequality keeps the relationship balanced.

Divide both sides of the inequality by the coefficient of

x

, which is

-3

x > 3

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

Determine the smallest integer that is strictly greater than 3.

Since the inequality is strict (

x > 3

), 3 is not included in the solution set. The smallest integer greater than 3 is 4.

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

Question