Linear Inequalities

Solve graphically 3x + 2y ≤150 x + 4y ≤ 80 x ≤15 y ≥ 0 x ≥ 0

How many litres of water will have to be added to 1125 litres of the 45% sol.
Of acid so that the resulting mixture will contain more than 25%but less than
30% acid content.

The water acidity in a pool is considered normal when the average Ph reading
of three daily measurements is between 7.2 and 7.8 If the first Ph reading are
7.48 and7.85, find the range of Ph value for the third reading that will result in
the acidity level being normal.

A man wants to cut three lengths from a single piece of board of length 91 cm.
The second length is to be 3 cm longer than the shortest and the third length
is to be twice as long as the shortest. What are the possible lengths of the
shortest board if the third piece is to be at least 5 cm longer than the second.

Solve graphically x - y ≤ 0

Solve 30x < 200when x is a natural no.

Solve 5x -3 ≤ 3x +1when x is an integer.

Solve graphically x + 2y ≤10 x + y ≥1 x - y ≤ 0

x ≥ 0, y ≥ 0

A sol. Of 8% boric acid is to be diluted by adding a 2% boric acid sol. 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% sol. how many litre of the 2% sol. will have to be
added.

In drilling world’s deepest hole it was found that the temperature T in degree

Celsius, x km below the surface of earth was given by

T = 30 + 25(x - 3),3 < x < 15At what depth will the tempt. Be between 200⁰ c

and 300⁰c

The longest side of aΔis 3 times the shortest side and the third side is 2 cm
shorter than the longest side. If the perimeter of theΔis at least 61 cm find the
minimum length of the shortest side.

Solve the inequalities 3x + 4y ≤12 graphically.

Solve 7x + 3 < 5x + 9 . Show the graph of the solution on number line.

Solution set of the in inequations 2x-1≤ 3and 3x+1≥-5 is

Solve graphically x - 2y ≤3 3x + 4y ≥12 x ≥ 0 y ≥1

A manufacturer has 600 litre of a 12% sol. Of acid. How many litres of a 30%
acid sol. Must be added to it so that acid content in the resulting mixture will
be more than 15% but less than 18%.

A company manufactures cassettes and its cost equation for a week is
C=300+1.5 x and its revenue equation is R=2 x , where x is the no. of cassettes
sold in a week. How many cassettes must be sold by the company to get some
profit?

Find all pairs of consecutive odd natural no. both of which are larger than 10
such that their sum is less than 40.

Solve 3x + 2y > 6 graphically

Solve 5x -3 < 3x +1when x is an integer.

Solve graphically 4x + 3≤ 60 y ≥  2x x ≥3 x, y ≥  0

A plumber can be paid under two schemes as given below.
I: Rs 600 and Rs 50 per hr.
II: Rs 170 per hr.
If the job takes n hr. for what values of n does the scheme I gives the plumber
the better wages.

Ravi obtained 70 and 75 mark in first unit test. Find the minimum marks he
should get in the third test to have an average of at least 60 marks.

Solve 3x - 6 ≥ 0graphically

Solve 3x +8 > 2when x is a real no.

A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second?

[Hint: If xis the length of the shortest board, then x, (x+ 3) and 2xare the lengths of the second and third piece, respectively. Thus, x= (x + 3) + 2x Ã¢”°Â¤91 and 2x Ã¢”°Â¥(x + 3) + 5]

 The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

 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 Sunita's marks in first four examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain in fifth examination to get grade 'A' in the course.

 Ravi obtained 70 and 75 marks in first two unit test. Find the minimum marks he should get in the third test to have an average of at least 60 marks.

 Solve the given inequality and show the graph of the solution on number line:

 Solve the given inequality for real x:

 Solve the given inequality for real x: 2(2x + 3) - 10 < 6 (x - 2)

Solve the given inequality for real x:

Solve the given inequality for real x: 

Solve the given inequality for real x: 3(2 - x) â”°Â¥ 2(1 - x)

Solve 3x+ 8 > 2, when

(i) xis an integer (ii) xis a real number

Solve 5x- 3 < 7, when

(i) xis an integer (ii) xis a real number

Solve -12x> 30, when

(i) xis a natural number (ii) xis an integer

Solve 24x < 100, when (i) x is a natural number (ii) x is an integer