Linear inequalities Practice Questions (Grade 9)

Question 1easy

What is the greatest integer value of $x$ for which $-2x > 6$ ?

Divide both sides by $-2$ and flip the inequality: $x < -3$ . The greatest integer less than $-3$ is $-4$ .

Question 2easy

Solve for $x$ : $x - 3 > 4$ . The solution is $x > k$ . What is the value of $k$ ?

Add 3 to both sides: $x > 7$ , so $k = 7$ .

Question 3easy

Solve for $x$ : $2x + 1 \le 9$ . The solution is $x \le k$ . What is the value of $k$ ?

Subtract 1: $2x \le 8$ . Divide by 2: $x \le 4$ , so $k = 4$ .

Question 4easy

Solve for $x$ : $4x + 1 > x + 10$ . The solution is $x > k$ . What is the value of $k$ ?

Subtract $x$ from both sides: $3x + 1 > 10$ . Subtract 1: $3x > 9$ . Divide by 3: $x > 3$ , so $k = 3$ .

Question 5easy

What is the least integer value of $x$ for which $-3x \le 12$ ?

Divide both sides by $-3$ and flip the inequality: $x \ge -4$ . The least integer that satisfies this is $-4$ .

Question 6easy

Solve for $x$ : $2x < 5$ . The solution is $x < k$ . What is the value of $k$ ?

Divide both sides by 2: $x < \dfrac{5}{2}$ , so $k = \dfrac{5}{2}$ .

Question 7easy

Solve for $x$ : $3x - 2 \ge 7$ . The solution is $x \ge k$ . What is the value of $k$ ?

Add 2: $3x \ge 9$ . Divide by 3: $x \ge 3$ , so $k = 3$ .

Question 8easy

Solve for $x$ : $5x - 3 \le 2x + 9$ . The solution is $x \le k$ . What is the value of $k$ ?

Subtract $2x$ from both sides: $3x - 3 \le 9$ . Add 3: $3x \le 12$ . Divide by 3: $x \le 4$ , so $k = 4$ .

Linear inequalities practice