Reasoning with Equations and Inequalities

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create two separate quadratic equations. Source: Avanti Yamamoto

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create a quadratic equation such that the distance between the solutions is greater than 1. Source: Mong Kon Mo

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box so that the solution(s) to the system are integers. Source: Ashley Taplin

Directions: Using the integers -9 to 9, at most one time each, place an integer in each box to create a system of equations as well as two solutions that make the system true. Source: Cody Pritchard

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make one set of functions intersect exactly twice, one set of functions intersect exactly once, and one set of functions never intersect. Source: Mike Fouchet

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create a correct sentence: The vertex of the parabola, y = ▢ x² + ▢ x + ▢, lies on the horizontal axis Source: Cecilia Calvo

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create a a system of equations with infinitely many solutions. Source: Mike

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create a problem that has the solutions x = 4 and x = -1/2. Source: Amy Herzog

Directions: Using the integers -9 to 9, at most one time each, place an integer in each box to create a system of inequalities as well as an included and excluded point. Make the points as close together as possible. Source: Robert Kaplinsky

Directions: Using the integers -9 to 9, at most one time each, place an integer in each box to create a system of inequalities as well as an included and excluded point. Source: Robert Kaplinsky