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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.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.
Let To earn a B in a mathematics course the test average must be at least 80% and less than 90%.
If a student earned 92%, 96%, 79%, and 83% on the first four tests, what must she score on the fifth test to earn a B?
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.
therefore there will be four lines in 1st quadrant.
Solving Linear Inequalities Word Problems
Now put (0,0) point in the inequality 2x 3y ≥ 6 ; x - 2y ≤ 2 ; 6x 4y ≤ 24 ; -3x 2y ≤ 3 , If it comes out true then feasible region of that inequality will be toward origin and if it comes out false then feasible region of that inequality will be away from origin . 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.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.This shows us that the numbers are ordered in a particular way.Those to the left are "less than" those to the right.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.This exercise practices word problems with systems of linear inequalities.Solve Graphically the System of Linear constraint 2x 3y ≥ 6 ; x - 2y ≤ 2 ; 6x 4y ≤ 24 ; -3x 2y ≤ 3 x≥ 0 ; y ≥ 0As from previous problems x ≥ 0 ; y ≥ 0 the common region from these two inequalities is in 1st quadrant.