How to Solve 9th Grade Linear Inequality problems

Friends! Today I am going to discuss about one of the most important and a bit complex topic of 9th standard mathematics which is inequality. Before proceeding further, we need to understand the basic concept behind inequality. In simplest mathematics manner we can say that inequality tells that two values are not equal for example: a ≠ b shows that a is not equal to b. Inequality problems comes with various inequality symbols. Before solving such kind of problems we need to learn the symbols of inequalities like the symbol < means less than and the symbol > means greater than and the symbol ≤ less than or equal to etc.

Now I am going to discuss about Linear Inequality. Graphing is the best way to understand the basic concept of Linear Inequality. A linear inequality graph describes an area of the coordinate plane that has a boundary line. In simple way in linear inequalities, everything is on one side of a line on a graph. In mathematics, a linear inequality is an inequality which involves a linear function.

Let’s take an example of 9th standard linear inequality topic to understand it better.
Solve the inequality: 4 – 3x ≤ 19
Now for solving this problem we need to subtract 4 from both sides
-3x ≤ 15
divide both the sides by 3 to get the desired solution:
-x ≤ 5
Another way of solving such a problem use following steps:
First: write the inequalities in a slope intercept form or in the form of y = mx + b.
Second: temporarily exchange the inequality symbol for the equal symbol
Third: Use different values for x to find points that will be graphed in the form (x,y).
At last: we need to draw lines on the graph using these above values. Point slope refers to a method of graphing a linear equation on an x-y axis.

How to plot Linear Inequality Graph

When linear equations are defined with some restriction which causes its answer to be in a fixed range then the situation is known as linear inequalities. This inequality is implemented in the equation with relations like greater than(>) or less than(<) and less than equal to(<=) or greater than equal to(>=) rather than equals to. Function of a linear inequality includes real number expression which is restricted by any constant integer through inequality relation:

H (x) < a or H (x) > a or H (x) ≤ a or H (x) ≥ a

The derivatives of the function are of variable x and range is decided according to constant 'a'.
The general representation form of linear inequality is as :
H(x)= c₀+ c₁x₁+ c₂x₂+............+c_nx_n< 0 or H(x)= c₀+ c₁x₁+ c₂x₂+............+c_nx_n ≤ 0
To implement the inequality graph for any linear inequality equation, firstly the calculation of the limits or range is required in which graph is to be plotted. After that the common required terms like intercepts of the Cartesian axes and slope of the line is calculated. When two inequality equations are joined together then the resultant equation is called compound inequality. The inequality graph of a compound inequality equation results in geographical area when it is being plotted on a 2D graph.
Generally compound inequities are joined with conduction(AND) and disjunction(OR) relations. For example:
x>2 AND y<2 in this compound relation there are two lines for x and y which includes the condition that value of x is can't be less than 2 and y is not greater than 2.

For having the solution of complex graphing related queries, students can use the online math tool which is available on various online math tutoring website, Graphing calculator. This tool uses the predefined computational steps which are installed in its program to solve particular type of query by Graphing functions.

Linear inequality and graphs

Friends today we are going to talk all about linear inequality and the way with which it can be easily solved. The term inequality generally means that two values are not equal to each other and thats why the is equal to sign (=) between them is replaced by comparison operators which are less than > or greater than < as: if a is not equal to b than it can be represent as : a< b or a> b

while using linear inequality in mathematical equations, the answer of the equation is also restricted in a fixed range which depends on the inequality sign and the integer value on the right side of the linear equation. Lets take an example of linear inequality problem as: x + 3 > 2 this means the solution of the equation must be greater than 2 and for this the value of x should not be less than 0 or we can say it should be positive.

The easiest way of solving linear inequality problems is inequality graphing. Graphing is a procedure with which the geographical form of any function, relation or equation is drawn for better explaining of them. While doing inequality graphing the straight line of linear inequality equation is restricted to only one side of the graph. For calculating the slope or tangent of the line we use the standard slope formula which is as:

M = y2 – y1/ x2 – x1

the slope of the line is basically equal to the Tangent which is determined by the differentiation of y with respect to x as Dy/Dx.

So M is also equals to Dy/Dx. The general form of any slope intercept is as the following :

Y = Mx + C

here C = Y intercept ( point on Y-axis where the graph crosses.)

Simple steps of graphing inequalities

Linear inequality in mathematics is an extended part of linear equations in which inequality involves. This inequality is initialized in the equation with the help of “greater than or less than” and “less than equal to or greater than equal to” relation instead of “equals to” .
The linear inequality function is a real number function and it is restricted by any real constant through inequality relation as:
g (x) < a or g (x) > a or g (x) ≤ a or g (x) ≥ a
here x is a variable whose value is a real number and 'a' is constant integer.
The common representation of linear inequality equation is as :
b₀+ b₁x₁+ b₂x₂+............+b_nx_n< 0 or b₀+ b₁x₁+ b₂x₂+............+b_nx ≤ 0
Inequality graph of any linear inequality equation includes the calculation of the limits according to which graphing of the equation is done in certain region of the graph. This limit is calculated according to the inequality sign in the equation.
The other required terms for graphing are co-ordinates of respected axes and slope of the line which are calculated in the similar manner as we do for linear equations.
For finding intersection or points at which line crosses the graph we use the X and Y intercept calculation and for slope of the line standard formula is used when we already have the endpoints of the line. Slope of the line is also can be calculated by Tangent of the line in the graph with respect to x-axis.
There is one more alternate to find these essential terms for doing graphing of linear inequities “ graphing calculator”, it is an online math tool provided by various math tutoring websites for solve math queries in a quick while. To learn more about linear inequalities students can use the math learning service provided by TutorVista website.

How to Graph Inequalities

In mathematics, a linear inequality is an inequality which involves a linear function. When two functions are defined using symbols like “greater then” or “less then” or “greater then equal to” and “less then equal to” then we get inequality expression. Linear inequalities are some how similar to linear equations. Let’s take an example of linear inequality which is involving a real number.

 f(x) < b or f(x) ≤ b

Here, f(x) is a linear function in real number and ‘b’ is a constant real number. Alternatively, it can be viewed as:

g(x) < 0 or g(x) ≤ 0,
 The above equations commonly expressed as:
a₀+ a₁x₁ + a₂x₂ +............+a_nx_n < 0
or,
a₀+ a₁x₁ + a₂x₂ +............+a_nx_n ≤ 0

Here x₁, x₂, x_3,....x_n are the unknown variables and a₁, a₂, …..a_n are the coefficients.
An Inequality graph can be draw by finding the limits of an equation. The inequality equation comes with the sign of less then or greater then so when we have to draw a graph which have to consider limits.

For graphing any equation we have to follow some steps.In the first steps, we have to locate ‘y’ intercept on the graph and locate the point. Then from this point we have to use the slope to find second point. After this, we darn a line that joins or connects the two points. With these steps we can easily plot a graph. Through graph we can also represent different equations.
The online tutoring service is a very good choice for the students to learn graphing of equation and other math topics. There are many websites available which are design to offer you online tutoring help. Tutorvista is an educational website which helps students in learning mathematics. The Tutorvista is mainly designed for those students who face problems in solving math problems and questions. Some websites also provides service of live tutors, by which students can interact directly with their tutors.

Graphing makes Linear Inequality easy

Friends, today we all are going to learn the basic concept behind linear inequality in mathematics and the graphing concepts used in an inequality graph. Before proceeding further let’s talk about inequality. Inequality basically tells that two values or expressions are not equal. For example, to understand it betterment a ≠ b shows that a is not equal to b. Slope formula plays an important role in graphing linear inequalities. So we need to know what slope formula means. Slope of a line describes the steepness, incline, or grade of the straight line. The slope through the points (x1, y1) and (x2, y2) is given as slope formula.

(m = y2-y1/x2-x1 ) where x1 is not equal to x2.
In general slope intercept form denotes the formula: y = mx + b.

where m = slope of the line

b = y intercept.
A linear inequality describes an area of the coordinate plane that has a boundary line. In simple way, in linear inequalities everything is on one side of a line on a graph.

In mathematics, a linear inequality is an inequality which involves a linear function. For solving inequalities we need to learn the symbols of inequalities like the symbol < means less than and the symbol > means greater than and the symbol ≤ less than or equal to etc.

Lets see an example to show a linear inequality graph. -4 < x - 2 < 8

Add 2 to all 3 parts in an equation

-4 < 2x < 10

Divide 2 from all 3 parts

-2 < x < 5

To graph the following equation, you put an open circle or we can say mark it by a dot on the point
(-2,0) and then you put an open circle on the point (5,0).Then draw a line between the two.