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# Reasoning with Equations and Inequalities

## Create an Inequality, Given a Solution Set

Directions: Write an inequality whose solution set is x < -1/2 by filling in the boxes with whole numbers 0 through 9, using each number at most once. Source: Daniel Luevanos

## Create a Quadratic Equation, Given Constraints

Directions: Write a quadratic equation that has a y-intercept of 24 and the distance between the x-intercepts is 10. Bonus: find more than 2 quadratic equations. Source: Daniel Luevanos

## Create an Equation with a Given Solution

Directions: Write three equations whose solution is -1/2 by filling in the boxes with whole numbers 0 through 9, using each number at most once for each equation. Source: Daniel Luevanos

## Systems of Equations – One Solution

Directions: Using the integers from -9 to 9, at most one time each, create a system of three-equations such that the solution is (1,1). Source: Audrey Mendivil, Daniel Luevanos, and Robert Kaplinsky

## Systems of Three Equations – Multiple Solutions

Directions: Using the digits 1 through 9, at most one time each, create a system of equations that has as many solutions as possible. Source: Audrey Mendivil, Daniel Luevanos, and Robert Kaplinsky

## Factoring Quadratics 2 – Fraction Solution

Directions: Fill in the empty boxes with whole numbers 0 through 9, using each number at most once, so that at least one of the solutions is a fraction. Source: Daniel Luevanos

## Factoring Quadratics – Fraction Solution

Directions: Fill in the empty boxes with whole numbers 0 through 9, using each number at most once, so that at least one of the solutions is a fraction. Source: Daniel Luevanos

## Factoring Quadratics 2 – Integer Solutions

Directions: Fill in the empty boxes with whole numbers 0 through 9, using each number at most once, so that the solutions are integers. Note that you can use a 05 to make a 5. Source: Daniel Luevanos