*At last mark common region from all the inequalities x ≥ 0 ; y ≥ 0 ; 3x 4y ≥ 12 and 4x 7y ≤ 28 and shade it , The shaded region will be the required/feasible region. *In the first four papers each of 100 marks, John got 95, 72, 73, 83 marks.Now Draw the graphs for two linear lines 2x 3y = 6 ; 6x 4y = 24 and -3x 2y = 3 .

*At last mark common region from all the inequalities x ≥ 0 ; y ≥ 0 ; 3x 4y ≥ 12 and 4x 7y ≤ 28 and shade it , The shaded region will be the required/feasible region. *In the first four papers each of 100 marks, John got 95, 72, 73, 83 marks.Now Draw the graphs for two linear lines 2x 3y = 6 ; 6x 4y = 24 and -3x 2y = 3 .

To show the inequality of numbers we use a symbolic notation: In the wiki Representation on the Real Line, we saw that real numbers can be visually represented on a number line, with each point on the line corresponding to a real number and each real number corresponding to a point on the line.

How can we use the number line to represent sets of real numbers?

This shows us that the numbers are ordered in a particular way.

Those to the left are "less than" those to the right.

is a mathematical statement that relates a linear expression as either less than or greater than another.

The following are some examples of linear inequalities, all of which are solved in this section: is a real number that will produce a true statement when substituted for the variable.When we draw regions of the number line, we use the following conventions: This example demonstrates that it may be necessary to perform algebraic manipulation to an inequality before being able to determine if the inequality represents a given region in the number line. Linear inequalities with one variable can be solved by algebraically manipulating the inequality so that the variable remains on one side and the numerical values on the other.Once this is done, we obtain a relationship that expresses the solution of the inequality.If he wants an average of greater than or equal to 75 marks and less than 80 marks, find the range of marks he should score in the fifth paper.It is easiest to understand inequalities in the context of a number line (see above).All but one of the techniques learned for solving linear equations apply to solving linear inequalities.You may add or subtract any real number to both sides of an inequality, and you may multiply or divide both sides by any As with all applications, carefully read the problem several times and look for key words and phrases. Next, translate the wording into a mathematical inequality.Therefore two points will be G(0,3/2) and H(-1,0) .Now plots both the points A(0,2) and B(3,0) in the plan and draw a line passing through these two points.We have seen that transforming inequalities into an equivalent inequality will lead us to the solution.To change an inequality into an equivalent inequality, we use the four basic arithmetic operations, but what operation to use is entirely dependent on the type of question, so we must keep our eyes sharp to identify what operation to use.

## Comments Solving Linear Inequalities Word Problems

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