linear Inequality :
we have studied linear equations in one and two variables, In early classes. In our daily life we often come across situation which were expressed in inequalities. In this chapter we will study linear inequalities which are very useful in solving problem in mathematics science engineering linear programming etc.
Inequations :
two algebraic expressions for two real numbers connected connected by the same ball `<,\ >,\geq,\leq` form and inequality
for example
(i) `x\geq4\;,\;\;y\leq3,\;x<5,\;y>6,\;2x+3y\leq4` etc are called literal inequalities.
(ii) `7>5,\;3<6,\;-3<-2` etc are called numerical inequalities.
(iii) `3\leq x<5,\;-4<y\leq3` etc are called double inequalities.
Rules for solving an inequation:
`\sqrt{2+3-4}`
(i) Adding or subtracting same number on both side of inequation does not change the inequality.
(ii) Multiplying or dividing both sides of an inequation by same (+) positive number does not change the inequality.
(iii) multiplying or dividing both side of an inequation by same (-) negative number inequality get reversed.
`\sqrt{2+3}`
`\sqrt{2+3}`