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.

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?

Solve the following system

x + 2y < 8 ….(i) 2x + y < 8

x ≥ 0 …(3)  y ≥ 0

Solve the inequation graphically 

Solve the inequations graphically&;y<–3.

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

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

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