2. Defination A Linear equation is an equation involving single variables or literals which have highest power 1, i.e. we have linear equation as one variable.
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4. Rule 2: Same quantity can be subtracted from both sides of the equation.
5. Rule 3: Both sides of an equation can be multiplied by the same number.
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7. Multiplication Changes to divisionExample: 5* = 20 5 * x = 20 (x is multiplied by 5 which on shifting 20 divides by 5) x= 20/5 x = 4 Division changes to MultiplicationExample: x/6 = 2 x= 2 X 6 (Division by 6 changes to multiplication by 6 on shifting) x = 12
16. Problem : A is twice as old as B. Three years ago A’s age was three times as of B find the age of A. Solution : let B’s age be x years, So A’s age = 2x Three years ago B’s Age = x-3 A’s Age = 2x-3 According to given condition 2x-3 = 3(x-3) 2x-3 = 3x-9 2x – 3x = -9 + 3 -x = -6 x = 6 B’s age = 6 years A’s age = 2*6 = 12 Years
17. mixed word problems Problem : One Number is 6 time the other. Their sum is 140 find the two numbers Solution let the other number be x then first number = 6x According to question 6x +x =140 7x =140 x = 140/7 x =20 First number = 6 *20 = 120 Other number = 20 Thus 120 & 20 are required two numbers
18. Problem : Gauri has a piggy bank it is full of 1 rupee and 50 paisa coins it contains three times as many 50 paisa coins as 1 rupee coins. The total amount in the piggy bank is 35 rupees how many coins are there of each kind in the piggy bank Solution: let the number of 1 rupee be x then the number of 50 paisa coins = 3x rupees 35 = 35 *100 paisa = 3500 paisa Rs. 1 = 100 paisa and x coins make 100x paisa coins of 50 paisa are 3x X 50 = 150 x paisa Total 250x paisa According to Question 250x = 3500 x = 3500/ 250 x= 14 Number of 1 Rupee Coin = 14 Number of 50 paisa coins = 3x = 3 X 14 = 42.
19. Problem: The length of a rectangle is 6m less than three times its breadth. Find the length and the breadth of the rectangle if its perimeter is 148m. Solution: Let the breadth of given rectangle be x m . Then , Length =(3x-6)m According to the question, Perimeter of Rectangle = 148m 2(3x-6+x)=148 2(4x-6)=148 8x-12=148 8x=148+12 8x=160 x=160/2=80
20. Problem: A 100 litre solution of acid and water contains 20 litres of acid. How many water must be added to make the solution 16% acidic? Solution: Let x litres of water be added to make the solution 16 % acidic. Then, the volume of solution = 100+x litres 16% of this is acid i.e, 16/100(100+x) = 20 litres 16(100+x)=20*100 1600+16x=2000 16x=2000-1600=400 x=400/16=25 litres
21. Problem: A number consists of 2 digits whose sum is 8. if 18 is added to it its digits are reversed. Find the number. Solution : Let the digit of the units place be x. then, the number at tens place=8-x original number = 10(8-x) +x = 80-10x+x =80-9x The reversed number = 10x+8-x =9x+8 According to question, 80-9x+18 = 9x+8 9x+9x=80+18-8 18x=90 x=90/18=5 Digit at units place = x = 5 And, digit at tens place = 8-x =8-5 =3 The number = 10*3+5 =30+5 =35