Question

Choose the correct description of the graph of the compound inequality

x - 2 > -4 and 3x less than or greater to 15

A number line with an open circle on -2, shading to the left, and a closed circle on 5, shading to the right.

A number line with a closed circle on -2, shading to the left, and an open circle on 5, shading to the right.

A number line with an open circle on -2, a closed circle on 5, and shading in between.

A number line with a closed circle on -2, an open circle on 5, and shading in between.

Answer 1

Felicia's doctor has put her on a diet of 500 calories per meal. This means she can consume no more than 500 calories at any meal. Her options for lunch in the cafeteria are as follows:

Yogurt that has 110 calories per serving
Mini Sandwiches that have 100 calories per serving

Which inequality below can be used to find the possible combinations of servings of yogurt (y) and mini sandwiches (s) she can eat and stay within her goal of no more than 500 calories?

110y + 100s greater than or equal to 500

110y - 100s greater than or equal to 500

110y + 100s less than or greater to 500

110y - 100s less than or greater to 500

Answer 2

Part 1: Solve the inequality 12 + 4x less than or greater to 5x - 2 and show all of your work. You can use <= to represent the less than or equal to symbol.
Part 2: Use complete sentences to describe the graph of the solution from Part 1. Be sure to include the type of circle and which direction the shading will be.