Linear Inequation — Formula Sheet

If the same number or expression is added to or subtracted from both sides of an inequation, the sign of inequality remains the same.

If both sides of an inequation are multiplied or divided by the same positive number, the sign of inequality remains the same.

If both sides of an inequation are multiplied or divided by the same negative number, the sign of inequality is reversed.

If both sides of an inequation are positive or both are negative, then on taking reciprocals, the sign of inequality reverses.

A term of the inequation can be shifted to other side by changing its sign and without changing the sign of inequality.

ax+b>0, ax+b<0, ax+b≥0, ax+b≤0 (a≠0)

ax+b>c, ax+b≥c, ax+b<c, ax+b≤c (a≠0)

-8 1/2 < 1/2 - 4x ≤ 7 1/2

-5(x-9)≥17-9x>x+2

7+3x≤35-2x with whole numbers gives a finite solution set.

2x-3/2≥6-5x with integers gives all integers from 2 onward.

A one-variable linear inequation can be written as ax+b>0, ax+b<0, ax+b≥0, or ax+b≤0, where a≠0.