Reasoning with Equations and Inequalities

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

Directions: Create 5 ordered pairs using the whole digits 0 – 9 exactly one time each. Then, create a linear inequality such that: 1. Two of the ordered pairs are solutions to the linear inequality. 2. Two of the ordered pairs are not solutions to the linear inequality. 3. One of the ordered pairs is on the boundary line but …

Directions: Using the digits 1 to 9, at most TWO times each, fill in the boxes to make an equation with no solutions. Source: Robert Kaplinsky

Directions: Fill each blank with a different integer such that the point (4,4) is within the solution region created by the constraints. Source: Erick Lee

Directions: Using the digits 1 to 9, at most one time each, fill in the boxes to create an equation such that the solution is as close to zero as possible. Source: Daniel Luevanos

Directions: Create an absolute value equation such that x = – 2 is an extraneous solution. Source: Daniel Luevanos

Directions: The black triangle is a right triangle with legs 8 and 6. The vertices are at the points (0,0), (0,8), and (6,0). The red line segment is perpendicular to hypotenuse. Find the length of the red line segment. Source: Kate Nerdypoo

Directions: Write at least two linear equations so that the solution of the system of equations of that line and 4x + y = 8 is (3, -4) Source: Nanette Johnson