Syllabus for Linear Inequation
(i) Linear Inequations Linear Inequations in one unknown for x ∈ N, W, Z, R. Solving
- Algebraically and writing the solution in set notation form.
- Representation of solution on the number line
Notes for Chapter Linear Equation
Inequalities signs
The mathematical statement in which we can say that the quantity on one side is not equal to the quantity on the
other side is called an inequation.
If a,b,c are the 3 real numbers ( I hope you know what is real number )
- ax + b > c in words you can read as ax + b is greater than c
- ax + b < c in words you can read as ax + b is less than c
- ax + b ≥ c in words you can read as ax + b is greater than or equal to c
- ax + b ≤ c in words you can read as ax + b is less than or equal to c
Here are some rules for Solving a Linear Inequality Algebraically:
Rule 1- When a positive term is moved from one side of an inequality to another, the sign of the term
becomes negative
5x + 2 > 8 = 5x > 8 -2
Rule 2- When a negative term is moved from one side of an inequality to another, the sign of the term becomes positive
5x – 2 > 8 = 2x > 8+2
Rule 3- When each term of an inequality is multiplied or divided by the same positive number (p), the sign of the inequality remains unchanged
x < y = px <py
x < y = x/p < y/p
Rule 4- When each term of an inequality is multiplied or divided by the same negative number (p), the
sign of the inequality reverses
x < y = px >py
x < y = x/p > y/p
Rule 5- If the sign of each term on both the sides of an inequality is changed, the sign of inequality gets
reversed
– x > 5 = x < – 5
Rule 6-If both the sides of an inequality are either positive or negative, then on taking their reciprocals, the sign of inequality reverses
x ≥ y = 1/x ≤ 1/y
Replacement & Solution Set
Replacement Set: The set, from which the values of the variable which are involved in the inequation, are chosen, is known as replacement set. (Think it as a Bucket of Small Balls)
Solution Set: A solution to an inequation is a number chosen from the replacement set which, satisfy the given inequation. The set of all solutions of an inequation is known as solution set of the inequation.
For example:
Let the given inequation be y < 6, if:
(i) The replacement set = N, the set of natural numbers;
The solution set = {1, 2, 3, 4, 5}.
(ii) The replacement set = W, the set of whole numbers;
The Solution set = {0, 2, 3, 4, 5}.
(iii) The replacement set = Z or I, the set of integers;
The solution set = {........., -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
ICSE Class 10 Linear Inequation Practice Questions
1. Solve the inequation : 5x – 2 ≤ 3(3 – x) where x ∈ { – 2, – 1, 0, 1, 2, 3, 4}. Also represent its solution on the number line.
2. Find the solution set of the inequation
x + 5 < 2 x + 3 ; x ∈ R
Graph the solution set on the number line.
3. Find positive integers which are such that if 6 is subtracted from five times the integer then the resulting number cannot be greater than four times the integer.
4. Find the range of values of a, which satisfy 7 ≤ – 4x + 2 < 12, x ∈ R. Graph these values of a on the real number line.
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