# Linear inequalities

In this section ask-math teaches you how to solve linear inequalities with one variable.
Some times its not possible to translate word problems in the form of equation so in such a case we may get certain statement involving a sign of inequality which are called 'inequations'
If x and y are any two quantities, in the equations there is x = y but if we get x ≠ y then it is called inequality.
If x ≠ y then any one of the following four conditions (relations) will be true.
either (i) x > y    (ii) x$\geq$ y    (iii) x < y   or    (iv) x $\leq$ y
Each of the above four conditions is an inequation.
In the same way, each of the following also represents an ineqation :
x < 8 ;   x $\geq$ 6 ;   x + 3 $\leq$7 7 ;   -x + 2 $\leq$ 11 etc.

## Linear inequalities in one variable

If a,b and c are real numbers, then each of the following is called a linear inequation in one variable : (i) ax - b > c , Read as ax - b is greater than c.
(ii) ax + b < c, Read as ax + b is less than c.
(iii) ax + b $\geq$ , Read as ax + b is greater than or equal c.
(iv) ax + b $\leq$ , Read as ax + b is less than or equal c.

In linear inequalities, the signs '>', '<', '$\leq$' and $\geq$ are called signs of inequality.

 Statement Meaning of statement Statement in mathematical form x is greater than a x is any value which is more than 'a' but not 'a'. x > a x is less than a x is any value which is less than 'a' but not 'a'. x < b x is at least a x is any value which is greater than 'a' and 'a' is included in it. x $\geq$ a x is at most a x is any value which is less than 'a' and 'a' is included in it. x $\leq$ a
Q.1 Writing inequations
1) The cost of a chair (x) is greater than or equal to $20. 2) x is less than 10. 3) 85 is greater than or equal to x. 4) The value of x is at most 35. 5) The value of x is at least 5. 6) -43 is greater than or equal to x. 7) The sum of 4x and 3x is at least 14. 8) If 3 times a number(x) is increased by 4, the result is at least 22. 9) x is at most 38. 10) Three times p plus 5 is at most 11. Answers 1) x$\geq$20 . 2) x < 10. 3) 85$\geq$x . 4) x$\leq$35 . 5) x$\geq$5 . 6) -43$\geq$x . 7) 4x + 3x$\geq$14 . 8) 3x + 4$\geq$22 . 9) x$\leq$38 . 10) 3p + 5$\leq\$ 11 .