class 11

Math

Algebra

Linear Inequalities

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0), is :

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Find all integers $x$ for which $(5x−1)<(x+1)_{2}<(7x−3)˙$

To receive Grade $A$ in a course, one must obtain an average of $90$ marks or more in five examinations (each of $100$ marks). If Sunitas marks in first four examinations are $87,92,94$ and $95$, find minimum marks that Sunita must obtain in the fifth examination to get grade $A$ in the course.

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

Solve the system of inequalities graphically:

Solve $x_{2}−x−2>0.$

Solve the following inequalities graphically in two-dimensional plane:$y+8≥2x$

Represent the solution of each of the following inequations on the real number line:$(2x+5)/3>3x−3$

Solve the inequalities$7<2(3x+11) ≤11$