7th Grade Two-Step Inequalities Quiz: 10 Questions with Explanations

A \(x < 5\)B \(x > 1\)C \(x > 15\)D \(x > 5\)

Add 6: \(3x > 15\); divide by 3: \(x > 5\).

A \(x > -4\)B \(x < -4\)C \(x > 4\)D \(x < 4\)

Dividing by -5 reverses the symbol: \(x > -4\).

A An open circle at 3 with shading to the leftB A closed circle at 3 with shading to the leftC A closed circle at 3 with shading to the rightD An open circle at 3 with shading to the right

At most 3 includes 3 (closed) and goes down (left).

A \(x \le 6\)B \(x \ge 6\)C \(x \ge 1.5\)D \(x \ge 22\)

Subtract 4: \(x/2 \ge 3\); multiply by 2: \(x \ge 6\).

A \(x = 4\)B \(x = 5\)C \(x = 3\)D \(x = 8\)

\(2(3) + 1 = 7 < 9\) is true. At 4, the value is 9, which is not less than 9.

A \(3g + 12 \ge 45\)B \(3g + 12 \le 45\)C \(3g + 12 > 45\)D \(3g – 12 \ge 45\)

At least means greater than or equal to, so use \(\ge\).

A \(x \ge 3\)B \(x \le 3\)C \(x \le 7\)D \(x \le 18\)

Divide by 4: \(x + 2 \le 5\); subtract 2: \(x \le 3\).

A \(x > -4\)B \(x < 4\)C \(x > 4\)D \(x < -4\)

Subtract 3: \(-x > 4\); multiply by -1 and reverse: \(x < -4\).

A \(n + 6 \le 40\)B \(n + 6 \ge 40\)C \(n + 6 < 40\)D \(n – 6 \le 40\)

At most means \(\le\), and the total is \(n + 6\).

A It includes 2B It includes only whole numbersC It includes 2.5 but not 2D It stops at 10

The solutions are all numbers greater than 2, so 2.5 works and 2 does not.