The term inequality applies to any statement involving one of the symbols<,>,≤,≥. Similar to ordinary equations, inequality equations too have solutions
Rules for finding the solutions to inequality equations
- Add or subtract at the same expression or number to both sides of the inequality and preserve the inequality sign.
- Multiply or divide both sides of the inequality by the same positive number and preserve the inequality sign.
- Multiply or divide both sides of the inequality by the same negative number and reverse the inequality sign.
The expression 3x – 1 > x + 1 is a linear inequality in one variable x. Thus, a linear inequality in x is an inequality in which the highest power of x is one (unity).
Solve the following linear inequality and represent them on a number line.
A number line is used to illustrate linear inequalities in one variable. A point x = a divides the number line into 2 parts, x < a and x > a
1. 4x + 8 < 3x + 16
Subtract 8 from both sides
4x + 8 – 8 < 3x – 8 + 16
4x < 3x + 8
Subtract 3x from both sides
4x – 3x < 3x + 8 – 3x
X < + 8
ii. 3 (x – 6) ≤ 9 (x – 1)
open the brackets
3x – 18 ≤ 9x – 9
Collect like terms
3x – 9x ≤ -9 + 18
-6x ≤ + 9
Divide through by -6 and change the sign.
(-6x)/(-6 ) ≥ (-9)/6
X ≥ (-3)/2
(x ≥ 23/7)
iii. 5 (x + 2) – 2(4x -1) > 6(2x -3)
iv. (5x-1)/3- (1-2x)/5 ≤8+x
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