text: # Linear Equations in One Variable
  
  ### Question:
  
  If 6x = 18, then 18x = 54.
  
  ### Linear Equations in One Variable
  
  8x-7-3x=6x-2x-3
  
  #### Q 2.
  
  The solution of the equation 3x – 4 = 1 – 2x is————- .
  
  #### Q 3.
  
  $frac { x }{ 5 } =frac { x-1 }{ 6 }$
  
  #### Q 4.
  
  $frac { 1 }{ 2 } left( x+1 ight) +frac { 1 }{ 3 } left( x-1 ight) =frac { 5 }{ 12 } left( x-2 ight)$
  
  #### Q 5.
  
  If x is an even number, then the next even number is 2(x +1).
  
  #### Q 6.
  
  If –$frac { 4 }{ 3 }$ y = –$frac { 3 }{ 4 }$ then y is equal to
  (a)$-{ left[ frac { 3 }{ 4 } ight] }^{ 2 }$ (b)$-{ left[ frac { 4 }{ 3 } ight] }^{ 2 }$
  (c)${ left[ frac { 3 }{ 4 } ight] }^{ 2 }$ (d)${ left[ frac { 4 }{ 3 } ight] }^{ 2 }$
  
  #### Q 7.
  
  When a number is divided by 8, the result is -3. The number is——–.
  
  #### Q 8.
  
  When 9 is subtracted from the product of p and 4, the result is 11. The value of p is—-.
  
  #### Q 9.
  
  The age of A is five years more than that of B. 5 years ago, the ratio of their ages was 3 :2. Find their present ages.
  
  #### Q 10.
  
  Find a number whose fifth part increased by 30 is equal to its fourth part decreased by 30.
  
  #### Q 11.
  
  0.4(3x-1)=0.5x +1
  
  #### Q 12.
  
  $frac { 3x+2 }{ 2x-3 } =-frac { 3 }{ 4 }$
  
  #### Q 13.
  
  If $frac { x }{ 11 }$ , then x=$frac { 11 }{ 15 }$.
  
  #### Q 14.
  
  After 12 years, Kanwar shall be 3 times as old as he was 4 years ago. Find his present age.
  
  #### Q 15.
  
  The solutoni of the equation ax + b = 0 is
  
  #### Q 16.
  
  $frac { 3x-8 }{ 2x } =1$
  
  #### Q 17.
  
  3 years ago, the age of boy was y years. His age 2 years ago was (y â€” 2) years.
  
  #### Q 18.
  
  $frac { y-(4-3y) }{ 2y-(3y+4y) } =frac { 1 }{ 5 }$
  
  10x-5-7x=5x+15-8
  
  #### Q 20.
  
  $frac { 9-3y }{ 1-9y } =frac { 8 }{ 5 }$
  
  #### Q 21.
  
  The sum of three consecutive numbers is 156. Find the number which is a multiple of 13 out of these numbers.
  
  #### Q 22.
  
  For what value of x is the perimeter of shape 186 cm?
  
  #### Q 23.
  
  Hamid has three boxes of different fruits. Box A weighs $2frac { 1 }{ 2 }$ kg more than box B and Box C weighs $10frac { 1 }{ 4 }$kg more than box B. The total weight of the three boxes is $48frac { 3 }{ 4 }$ kg. How many kilograms does box A weigh?
  
  #### Q 24.
  
  If $frac { 2 }{ 5 }$ x-2=5-$frac { 3 }{ 5 }$ x,then x=——-.
  
  #### Q 25.
  
  4 (3p + 2) – 5 (6p – 1) = 2 (p – 8) – 6 (7p – 4)
  
  #### Q 26.
  
  The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volumes of water in each tank.
  
  #### Q 27.
  
  The sum of four consecutive integers is 266. What are the integers?
  
  #### Q 28.
  
  A lady went to a bank with Rs 100000. She asked the cashier to give her Rs 500 and Rs 1000 currency notes in return. She got 175 currency notes in all. Find the number of each kind of currency notes.
  
  #### Q 29.
  
  For what value of x is the perimeter of shape 77 cm?
  
  #### Q 30.
  
  When 9 is subtracted from the product of p and 4, the result is 11. The value of p is—-.
  
  #### Q 32.
  
  The value of S in $frac { 1 }{ 3 }$ + S = $frac { 2 }{ 5 }$ is
  (a)$frac { 4 }{ 5 }$ (b)$frac { 1 }{ 15 }$
  (c)10 (d)0
  
  #### Q 33.
  
  Convert the statement ‘adding 15 to 4 times x is 39’ into an equation.
  
  #### Q 34.
  
  The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 and the denominator is decreased by 1, then expression for new denominator is——.
  
  #### Q 35.
  
  Distance between two places A and B is 210 km. Two cars start simultaneously from A and B in opposite directions and distance between them after 3 hours is 54 km. If speed of one car is less than that of other by 8 km/h, then find the speed of each.
  
  #### Q 36.
  
  If $frac { 5x }{ 3 }$-4 =$frac { 2x }{ 5 }$ , then the numerical value of 2x – 7 is
  (a)$frac { 19 }{ 13 }$ (b)$frac { -13 }{ 19 }$
  (c)0 (d)$frac { 13 }{ 19 }$
  
  #### Q 37.
  
  Which of the following is a linear expression?
  (a) ${ x }^{ 2 }$ +1 (b) y + ${ y }^{ 2 }$
  (c) 4 (d) 1 + z
  
  #### Q 38.
  
  The number of boys and girls in a class are in the ratio 5 : 4. If the number of boys is 9 more than the number of girls, then number of boys is 9.
  
  4t-3-(3t+1)=5t-4
  
  #### Q 40.
  
  $frac { x }{ 2 } -frac { 1 }{ 4 } left( x-frac { 1 }{ 3 } ight) =frac { 1 }{ 6 } left( x+1 ight) +frac { 1 }{ 12 }$
  
  #### Q 41.
  
  The shifting of a number from one side of an equation to other is called
  (a) transposition (b) distributivity
  (c) commutativity (d) associativity .
  
  #### Q 42.
  
  If a and b are positive integers, then the solution of the equation ax = b has to be always
  (a) positive (b) negative (c) one (d) zero
  
  #### Q 43.
  
  The solution of the equation 2y = 5y-$frac { 18 }{ 5 }$ is————.
  
  #### Q 44.
  
  A and B are together 90 years old. Five years ago, A was thrice as old as B was. Hence, the ages of A and B five years back would be (x – 5) years and (85 – x) years, respectively.
  
  #### Q 45.
  
  If 8x – 3 = 25 + 17x, then x is
  (a) a fraction (b) an integer
  (c) a rational number (d) Cannot be solved
  
  #### Q 46.
  
  Three consecutive numbers whose sum is 12 are——–,————-and———.
  
  #### Q 47.
  
  A term of an equation can be transposed to the other side by changing its—-.
  
  #### Q 48.
  
  On subtracting 8 from x, the result is 2. The value of x is——–.
  
  #### Q 49.
  
  Shikha’s present age is p years. Reemu’s present age is 4 times the present age of Shikha. After 5 years, Reemu’s age will be 15p years.
  
  #### Q 50.
  
  Sum of the ages of Anju and her mother is 65 years. If Anju’s present age is y years, then her mother’s age before 5 years is (60 – y) years.
explanation: The document is a collection of multiple math questions, primarily focusing on linear equations in one variable. Each question is labeled with a number and is presented in a structured format. There are no answers provided for these questions.
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distilabel_metadata.content: # Linear Equations in One Variable
  
  ### Question:
  
  If 6x = 18, then 18x = 54.
  
  ### Linear Equations in One Variable
  
  8x-7-3x=6x-2x-3
  
  #### Q 2.
  
  The solution of the equation 3x – 4 = 1 – 2x is————- .
  
  #### Q 3.
  
  $frac { x }{ 5 } =frac { x-1 }{ 6 }$
  
  #### Q 4.
  
  $frac { 1 }{ 2 } left( x+1 ight) +frac { 1 }{ 3 } left( x-1 ight) =frac { 5 }{ 12 } left( x-2 ight)$
  
  #### Q 5.
  
  If x is an even number, then the next even number is 2(x +1).
  
  #### Q 6.
  
  If –$frac { 4 }{ 3 }$ y = –$frac { 3 }{ 4 }$ then y is equal to
  (a)$-{ left[ frac { 3 }{ 4 } ight] }^{ 2 }$ (b)$-{ left[ frac { 4 }{ 3 } ight] }^{ 2 }$
  (c)${ left[ frac { 3 }{ 4 } ight] }^{ 2 }$ (d)${ left[ frac { 4 }{ 3 } ight] }^{ 2 }$
  
  #### Q 7.
  
  When a number is divided by 8, the result is -3. The number is——–.
  
  #### Q 8.
  
  When 9 is subtracted from the product of p and 4, the result is 11. The value of p is—-.
  
  #### Q 9.
  
  The age of A is five years more than that of B. 5 years ago, the ratio of their ages was 3 :2. Find their present ages.
  
  #### Q 10.
  
  Find a number whose fifth part increased by 30 is equal to its fourth part decreased by 30.
  
  #### Q 11.
  
  0.4(3x-1)=0.5x +1
  
  #### Q 12.
  
  $frac { 3x+2 }{ 2x-3 } =-frac { 3 }{ 4 }$
  
  #### Q 13.
  
  If $frac { x }{ 11 }$ , then x=$frac { 11 }{ 15 }$.
  
  #### Q 14.
  
  After 12 years, Kanwar shall be 3 times as old as he was 4 years ago. Find his present age.
  
  #### Q 15.
  
  The solutoni of the equation ax + b = 0 is
  
  #### Q 16.
  
  $frac { 3x-8 }{ 2x } =1$
  
  #### Q 17.
  
  3 years ago, the age of boy was y years. His age 2 years ago was (y â€” 2) years.
  
  #### Q 18.
  
  $frac { y-(4-3y) }{ 2y-(3y+4y) } =frac { 1 }{ 5 }$
  
  10x-5-7x=5x+15-8
  
  #### Q 20.
  
  $frac { 9-3y }{ 1-9y } =frac { 8 }{ 5 }$
  
  #### Q 21.
  
  The sum of three consecutive numbers is 156. Find the number which is a multiple of 13 out of these numbers.
  
  #### Q 22.
  
  For what value of x is the perimeter of shape 186 cm?
  
  #### Q 23.
  
  Hamid has three boxes of different fruits. Box A weighs $2frac { 1 }{ 2 }$ kg more than box B and Box C weighs $10frac { 1 }{ 4 }$kg more than box B. The total weight of the three boxes is $48frac { 3 }{ 4 }$ kg. How many kilograms does box A weigh?
  
  #### Q 24.
  
  If $frac { 2 }{ 5 }$ x-2=5-$frac { 3 }{ 5 }$ x,then x=——-.
  
  #### Q 25.
  
  4 (3p + 2) – 5 (6p – 1) = 2 (p – 8) – 6 (7p – 4)
  
  #### Q 26.
  
  The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volumes of water in each tank.
  
  #### Q 27.
  
  The sum of four consecutive integers is 266. What are the integers?
  
  #### Q 28.
  
  A lady went to a bank with Rs 100000. She asked the cashier to give her Rs 500 and Rs 1000 currency notes in return. She got 175 currency notes in all. Find the number of each kind of currency notes.
  
  #### Q 29.
  
  For what value of x is the perimeter of shape 77 cm?
  
  #### Q 30.
  
  When 9 is subtracted from the product of p and 4, the result is 11. The value of p is—-.
  
  #### Q 32.
  
  The value of S in $frac { 1 }{ 3 }$ + S = $frac { 2 }{ 5 }$ is
  (a)$frac { 4 }{ 5 }$ (b)$frac { 1 }{ 15 }$
  (c)10 (d)0
  
  #### Q 33.
  
  Convert the statement ‘adding 15 to 4 times x is 39’ into an equation.
  
  #### Q 34.
  
  The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 and the denominator is decreased by 1, then expression for new denominator is——.
  
  #### Q 35.
  
  Distance between two places A and B is 210 km. Two cars start simultaneously from A and B in opposite directions and distance between them after 3 hours is 54 km. If speed of one car is less than that of other by 8 km/h, then find the speed of each.
  
  #### Q 36.
  
  If $frac { 5x }{ 3 }$-4 =$frac { 2x }{ 5 }$ , then the numerical value of 2x – 7 is
  (a)$frac { 19 }{ 13 }$ (b)$frac { -13 }{ 19 }$
  (c)0 (d)$frac { 13 }{ 19 }$
  
  #### Q 37.
  
  Which of the following is a linear expression?
  (a) ${ x }^{ 2 }$ +1 (b) y + ${ y }^{ 2 }$
  (c) 4 (d) 1 + z
  
  #### Q 38.
  
  The number of boys and girls in a class are in the ratio 5 : 4. If the number of boys is 9 more than the number of girls, then number of boys is 9.
  
  4t-3-(3t+1)=5t-4
  
  #### Q 40.
  
  $frac { x }{ 2 } -frac { 1 }{ 4 } left( x-frac { 1 }{ 3 } ight) =frac { 1 }{ 6 } left( x+1 ight) +frac { 1 }{ 12 }$
  
  #### Q 41.
  
  The shifting of a number from one side of an equation to other is called
  (a) transposition (b) distributivity
  (c) commutativity (d) associativity .
  
  #### Q 42.
  
  If a and b are positive integers, then the solution of the equation ax = b has to be always
  (a) positive (b) negative (c) one (d) zero
  
  #### Q 43.
  
  The solution of the equation 2y = 5y-$frac { 18 }{ 5 }$ is————.
  
  #### Q 44.
  
  A and B are together 90 years old. Five years ago, A was thrice as old as B was. Hence, the ages of A and B five years back would be (x – 5) years and (85 – x) years, respectively.
  
  #### Q 45.
  
  If 8x – 3 = 25 + 17x, then x is
  (a) a fraction (b) an integer
  (c) a rational number (d) Cannot be solved
  
  #### Q 46.
  
  Three consecutive numbers whose sum is 12 are——–,————-and———.
  
  #### Q 47.
  
  A term of an equation can be transposed to the other side by changing its—-.
  
  #### Q 48.
  
  On subtracting 8 from x, the result is 2. The value of x is——–.
  
  #### Q 49.
  
  Shikha’s present age is p years. Reemu’s present age is 4 times the present age of Shikha. After 5 years, Reemu’s age will be 15p years.
  
  #### Q 50.
  
  Sum of the ages of Anju and her mother is 65 years. If Anju’s present age is y years, then her mother’s age before 5 years is (60 – y) years.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a collection of multiple math questions, primarily focusing on linear equations in one variable. Each question is labeled with a number and is presented in a structured format. There are no answers provided for these questions.
  
  Label: multiple-question