# Reasoning with Equations and Inequalities

## Linear Inequalities in Two Variables

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 …

## Solving Equations with Variables on Both Sides

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

## System of Inequalities

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

## Create an Equation with a Solution Closest to Zero

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

## Absolute Value Equation

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

## Finding the Length of a Right Triangle’s Altitude

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

## Create a System of Equations, Given 1 Equation and the Solution

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

## Create an Inequality, Given a Solution Set

Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to create an inequality whose solution set is x < -1/2. Source: Daniel Luevanos