Solutions to Equations and Inequalities

Elena is ordering dried chili peppers and corn husks for her cooking class. Chili peppers cost $16.95 per pound and corn husks cost $6.49 per pound. Elena spends less than $50 on d pounds of dried chili peppers and h pounds of corn husks. Here is a graph that represents this situation. Write an inequality that represents this situation. Can Elena purchase 2 pounds of dried chili peppers and 4 pounds of corn husks and spend less than $50? Explain your reasoning. Can Elena purchase 1.5 pounds of dried chili peppers and 3 pounds of corn husks and spend less than $50? Explain your reasoning.

A farmer is creating a budget for planting soybeans and wheat. Planting soybeans costs $200 per acre and planting wheat costs $500 per acre. He wants to spend no more than $100,000 planting soybeans and wheat. Write an inequality to describe the constraints. Specify what each variable represents.

Name one solution to the inequality and explain what it represents in that situation.

What is the solution to this inequality?

• x > −18

• x > 9

• x > 21

• x > −42

-3y + 2 > 11

• y < -3

• y > -3

• y < 3

• y > 3

• A

• B

• C

• D

​ (a)   ​ is a solution to y = x + 3

• (4,7)

• (2,6)

• (6,3)

• (5,2)

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

Find the value of x:

• x > 2

• x < 2

• x > -10

• x > 10