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 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: Use only the digits 1-9, each digit only once, 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

Directions: Using the integers −9 to 9 at most one time each, place an integer in each box to create a system of equations whose solution is as close to the origin 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 equations and its solution. Source: Robert Kaplinsky

Directions: Using the digits 1 to 9, at most one time each, make two compound inequalities that are equivalent to 2 ≤ x < 4. Source: Robert Kaplinsky

Directions: Using the digits 1 to 9, at most one time each, make a compound inequality that has the largest interval. Source: Robert Kaplinsky

Directions: Using the digits 1 to 30, at most one time each, fill in the boxes to create a system of two linear equations where (3, 2) is the solution to the system. Source: Daniel Luevanos