Toll free: 1- 877- 252 - 7763 | Fax: 1- 425- 458- 9358

# Get customized homework help now!

System of Inequalities

Inequalities:

A number a > a number b if a - b is positive.

i.e. a > b

Example: 2 > 1 because 2-1 = 1 is positive.

-1 > 2 is false because -1-2 = -3 is negative.

Rules for inequalities:

• An equal quantity may be added to, (or subtracted from) both sides of an inequality without changing the inequality.
4 > -1
4-3 >-1-3(subtract 3)
1 > -2 which is also true.
• An equal positive quantity may multiply (or divide) both sides of an inequality without changing the inequality.
4 > -1
4 x 2 > -1 x 2(multiply by 2)
8 > -2 which is also true.
• If both sides of an inequality are multiplied ( or divided by a negative quantity then the inequality is reversed.
4 > -1
4 x -3 < -1 x -3(multiply by -3; sign reversed)
-12 < 3 which is true.

Solving inequalities:

• x-5 = 0 gives x=5
• x-5 > 7
x-5+5 > 7+5 ( add 5 on both sides)
x > 12
• 2x-2 < x
2x-2+2 < x+2 ( add 2 on both sides)
2x < x+2
2x-x < x+2-x (subtract x on both sides)
x<2

Definition of System of Inequalities

• A system of inequalities is a set of two or more inequalities with the same variables, graphed in the same coordinate plane.

Examples of System of Inequalities

The figure below shows the graph of the system of inequality y ≤ x+2

The figure below shows the graph of the system of inequalities 2x - 6y < 12, 3x + 4y < 12, and 4x + 2y ≥ 8.

Choose the correct graph:

Which of the graphs defines the system of inequalities, x + y < 3, - 5x + 2y ≤ 10, y ≥ - 3?

Solution:
Step 1: Graph all the three inequalities in the same coordinate plane.

Step 2: The graph of x + y < 3 is the half-plane below the dashed line x + y = 3.
Step 3: The graph of - 5x + 2y ≤ 10 is the half-plane on and below the solid line - 5x + 2y = 10.
Step 4: The graph of y ≥ - 3  is the half-plane on and above the solid line y = - 3.
Step 5: The graph of the system is the intersection of the three half planes as shown in the graph.
Step 6: Graph-1 is the correct answer.

25% OFF on Homework Help
Name* :
Email* :
Country* :
Phone* :
Subject* :
Due Date*
Time
AM/PM
Timezone
Type Your Questions OR Instructions Below
 (Type Security Code - case sensitive)
Note: We will not do your assignment for you. We will only help you understand the steps to solve it.
 Courses/Topics we help on Discrete Mathematics Applied Calculus I Applied Calculus II Healthcare Statistics and Research Advanced Engineering Mathematics I Advanced Engineering Mathematics II Introduction to Algebra Basic Algebra Algebra for College Students Algebra for College Students Pre-Calculus Statistics for Decision-Making Polar Co-ordinates Area in Polar Coordinates Solving Systems of Equations Systems of Inequalities Quadratic Equations Matrices and System of Equations The Determinant of a Square Matrix Cramer's Rule Ellipse Hyperbola Rate of Change Measurement of Speed Finding Limits Graphically Higher Order Derivatives Rolle's Theorem and Mean Value Theorem Concavity and Second Derivative Test Limits at Infinity Indefinite Integration Definite Integration Integration by Substitution Area of a Region Between Two Curves Volume by Shell Method and Disc Method Integration by Parts Trigonometric Integration Differential Equations Slope Fields Growth and Decay System of Differential Equations Parametric Equations Complex Numbers The Inverse of a Square Matrix Parabola Functions and Their Graphs Evaluating Limits Analytically Increasing and Decreasing Functions Newton's Method Finding Area Using Integration Numerical Integration Moments Partial Fractions Separation of Variables Second Order Differential Equations IB Maths