Linear Inequalities in Mathematics: Rules and Solutions
Explore the study of linear inequalities in mathematics, covering topics such as rules for solving inequalities, algebraic solutions, and graphical representations using number lines. Understand how to manipulate inequalities with equal and unequal signs.
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an International CBSE Finger Print School Coimbatore SUBJECT NAME- 041 MATHEMATICS GRADE-XI UNIT 6 TOPIC LINEAR INEQULATIES LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY 12/06/23 1
LINEAR INEQULATIES INEQUALITY Two real numbers or two algebraic expressions related by the symbol <(less than), > (greater than), (less than equal to) or (greater than equal to) form an inequality. 12/06/23 2/16 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
But in this chapter we shall confine to the study of linear inequalities in one and two variables only. RULES FOR SOLVING AN INEQUALITY Rule1:Equal numbers may be added to (or substracted from) both sides of an inequality without effecting the sign of inequality Ex2: 3<10 Subtracting 2 both sides 3-2<10-2 1<8 Ex1: 3<10 Adding 5 both sides 3+5<10+5 8<15 12/06/23 3/16 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
Rule 2:Both sides of an inequality can be multiplied (or divided) by the same positive number, it does not effect the sign of inequality Ex 1: 10>8 Multiply by 5 both sides 10x5>8x5 50>40 Rule 3:Both sides of an inequality is multiplied or divided by a negative number, then the sign of inequality is reversed Ex: 6<8 Multiply by -5 both sides 6x(-5)>8x(-5) -30>-40 12/06/23 4/16 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
ALGEBRIC SOLUTION OF LINEAR INEQUALITIES The values of x which makes the inequality a true statement are called solution of inequality and the set of x values is called solution set of inequality. 12/06/23 5/16 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
Number Lines Graphical Representation To represent x<a (or x>a) on a number line, put a circle on the number a and dark line to the left (or right) of the number a. X>2 -1 -2 0 1 3 4 2 X<2 -1 -2 0 1 3 4 2 12/06/23 6/16 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
To represent xa (or xa) on a number line, put a dark circle on the number a and dark line to the left (or right) of the number a. X 1 -1 -2 0 1 3 4 2 X - 2 -1 -2 0 1 3 4 2 12/06/23 7/16 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
While solving word problems > < Is more than Is greater than Is larger than Above Minimum At least Is not less than Not smaller than Is smaller than Is less than Below Maximum At most Not more than Is not greater than 12/06/23 8/16 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
Graphical Solution of Linear Inequalities in Two Variables A vertical line will divide the plane in left and right half planes Y 3 Right half Plane Left half Plane 2 1 0 -1 1 3 4 X 2 -1 -2 -3 Y 9/16 12/06/23 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
non-vertical line will divide the plane into lower and upper half planes 12/06/23 10/16 10 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
Graphical Solution of Linear Inequalities in Two Variables If an inequality is having or symbol, then the points on the line are also included in the solutions of the inequality and the graph of the inequality lies left (below) or right (above) of the graph of the inequality represented by dark line that satisfies an arbitrary point in that part. 11/16 12/06/23 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
12/06/23 12/16 12 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
Graphical Solution of Linear Inequalities in Two Variables If an inequality is having < or > symbol, then the points on the line are not included in the solutions of the inequality and the graph of the inequality lies to the left (below) or right (above) of the graph of the corresponding equality represented by dotted line that satisfies an arbitrary point in that part. 12/06/23 13/16 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
12/06/23 14/16 14 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
Questions: 1. Solve 4x + 3 < 6x +7. 2. 3. Find all pairs of consecutive odd natural numbers, both of which are larger than 10, such that their sum is less than 40. 4. A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18%? 12/06/23 15/16 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
References https://www.powershow.com/view4/582cfe- NmJkM/Solving_Linear_Inequalities_powerpoint_ppt_presentation https://edurev.in/studytube/Chapter-6-Linear-Inequalities-PowerPoint- Presentat/33cc885e-6c17-4f34-b7ac-1f1d450a2245_p https://www.teachmint.com/tfile/studymaterial/class- 11th/mathematics/ppt116thchapterpptx/e521f967-52bf-4b39-963c-b97615258ab5 https://www.toppr.com/bytes/wp-content/uploads/2018/03/Ch-06_Linear- Inequalities.pdf https://schools.aglasem.com/ncert-books-class-11-maths-chapter-6/ 12/06/23 16/16 16 LINEAR INEQULATIES/041 MATHEMATHICS/MADHANKUMAR A /MATHS/SNS ACADEMY
