Linear Inequalities

Solve the following system of Linear inequalities graphically.

x + y ≥ 5 … (1),

x + y ≤ –5… (2)

Solve and graph the solution of 5 – 3x & ≤ & 13 + x.

Solve the following system

x + 2y < 8 ….(i) 2x + y < 8

x ≥ 0 …(3)  y ≥ 0

Find all pairs of consecutive even positive integers, both of which are larger than 8, such that their sum is less than 25.

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

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

Solve 30x < 200 when:

(i) x is a natural number

(ii) x is an integer

Solve the inequation graphically 

Solve the inequations graphically&;y<–3.

Solve −15 < ^{3(x − 2)}/₅ ≤ 0

Solve and graph the solution of  2x – 6 < 2.

Exhibit graphically the solution set of the linear inequations

x + y ≤ 5, 4x + y ≥ 4, x + 5y ≥ 5, x ≤ 4, y ≤ 3