How Do You Solve a Word Problem Using a System of Inequalities?

Note:

Math can sneak up in all sorts of places, so it's important to be prepared! Follow this tutorial to see a real world math problem involving a system of inequalities!

Keywords:

Solution
Problem
inequalities
system of inequalities
linear
solve
word problem

Background Tutorials

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
- What's an Inequality?
  
  Inequalities come up all the time when you're working algebra problems. In this tutorial you'll learn what an inequality is, and you'll see all the common inequality symbols that you're likely to see :)
Write expressions that record operations with numbers and with letters standing for numbers.
- How Do You Translate a Phrase with One Variable and Number Into a Mathematical Expression?
  
  Need some practice translating phrases into mathematical expressions? Then this tutorial is for you! You'll get practice translating statements involving addition, subtraction, multiplication, or division into mathematical expressions.
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
- How Do You Evaluate an Algebraic Expression?
  
  Plugging variables into an expression is essential for solving many algebra problems. See how to plug in variable values by watching this tutorial.
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
- How Do You Solve a Word Problem By Writing an Inequality?
  
  Got an inequality in a word problem? This tutorial will show you how to define variables, translate a word problem into an inequality, and understand what it all means!
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
- What's Slope-Intercept Form of a Linear Equation?
  
  When you're learning about linear equations, you're bound to run into the point-slope form of a line. This form is quite useful in creating an equation of a line if you're given the slope and a point on the line. Watch this tutorial, and learn about the point-slope form of a line!
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- How Do You Graph a Line in Slope-Intercept Form?
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
- What Are Some Words We Use To Write Inequalities?
  
  Knowing the definition for a compound inequality is one thing, but being able to identify one in a word problem or phrase can be an entirely different challenge. Arm yourself by learning some of the common phrases used to describe a compound inequality and an absolute value inequality.
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
- What's a System of Linear Inequalities?
  
  A system of equations is a set of equations with the same variables. A system of inequalities is almost exactly the same, except you're working with inequalities instead of equations! To solve such a system, you need to find the variable values that will make each inequality true at the same time. This tutorial will introduce you to systems of inequalities.
- How Do You Graph a Greater Than Inequality on the Coordinate Plane?
  
  Graphing inequalities on the coordinate plane is not as difficult as you might think, especially if you know what to do! In this tutorial, you'll see the steps you need to follow to graph an inequality.
- How Do You Determine if an Ordered Pair is a Solution to a Linear Inequality?
  
  To see if an ordered pair is a solution to an inequality, plug it into the inequality and simplify. If you get a true statement, then the ordered pair is a solutio
Graph linear and quadratic functions and show intercepts, maxima, and minima.
- How Do You Graph a Vertical Line?
  
  To graph a vertical line that goes through a given point, first plot that point. Then draw a straight line up and down that goes through the point, and you're done! To see this process in action, watch this tutorial!
- How Do You Graph a Horizontal Line?
  
  To graph a horizontal line that goes through a given point, first plot that point. Then draw a straight line left and right that goes through the point, and you're done! To see this process in action, watch this tutorial!

How Do You Solve a Word Problem Using a System of Inequalities?

How Do You Solve a Word Problem Using a System of Inequalities?

Note:

Keywords:

Background Tutorials

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Write expressions that record operations with numbers and with letters standing for numbers.

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Graph linear and quadratic functions and show intercepts, maxima, and minima.

Further Exploration

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.