Mathematics

Linear Equations in One Variable

Question:

10x-5-7x=5x+15-8

Answer:

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-19

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Linear Equations in One Variable

Q 1.

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 2.

8x-7-3x=6x-2x-3

Q 4.

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 5.

Which of the following is a linear expression?
(a) { x }^{ 2 } +1 (b) y + { y }^{ 2 }
(c) 4 (d) 1 + z

Q 6.

If the sum of two consecutive numbers is 93 and one of them is x, then the other number is 93 – x.

Q 8.

When a number is divided by 8, the result is -3. The number is——–.

Q 9.

If  frac { 2 }{ 5 } x-2=5- frac { 3 }{ 5 } x,then x=——-.

Q 10.

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.

Q 11.

1-(x-2)-[(x-3)-(x-1)]=0

Q 12.

Rs 13500 are to be distributed among Salma, Kiran and Jenifer in such a way that Salma gets Rs 1000 more than Kiran and Jenifer gets Rs 500 more than Kiran. Find the money received by Jenifer.

Q 13.

Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.

Q 14.

When 9 is subtracted from the product of p and 4, the result is 11. The value of p is—-.

Q 15.

If  frac { 2 }{ 5 } x-2=5- frac { 3 }{ 5 } x,then x=——-.

Q 16.

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.

Q 17.

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-1

Q 18.

If 6x = 18, then 18x = 54.

Q 19.

frac { 5x }{ 2x-1 } =2

Q 20.

 frac { y-(4-3y) }{ 2y-(3y+4y) } =frac { 1 }{ 5 }

Q 21.

0.4(3x-1)=0.5x +1

Q 22.

5(x-1)-2(x+8)=0

Q 23.

 frac { 5x+1 }{ 2x } =-frac { 1 }{ 3 }

Q 24.

frac { 3t-2 }{ 3 } +frac { 2t+3 }{ 2 } =t+frac { 7 }{ 6 }

Q 25.

The sum of three consecutive odd natural numbers is 69. Find the prime number out of these numbers.

Q 26.

The value of x, for which the expressions 3x – 4 and 2x + 1 become equal, is
(a) -3 (b) 0
(c) 5 x (d) 1

Q 27.

15 The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.(a) 112 (b) 126 (c) 119 (d) 116

Q 28.

Any value of the variable, which makes both sides of an equation equal, is known as a———–of the equation.

Q 29.

A term of an equation can be transposed to the other side by changing its—-.

Q 30.

If x is an even number, then the next even number is 2(x +1).

Q 31.

frac { 0.2x+5 }{ 3.5x-3 } =frac { 2 }{ 5 }

Q 32.

4t-3-(3t+1)=5t-4

Q 33.

The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20%, then we get the same perimeter. Find the length and breadth of the rectangle.

Q 34.

In questions 16 to 32, fill in the blanks to make each statement true.
Question. 16 In a linear equation, the——— power of the variable appearing in the equation is one.

Q 35.

The solution of the equation 3x – 4 = 1 – 2x is————- .

Q 36.

After 18 years, Swarnim will be 4 times as old as he is now. His present age is——–.

Q 37.

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 38.

The sum of two consecutive multiples of 10 is 210. The smaller multiple is——-.

Q 39.

In the equation 2x = 4 – x, transposing – x to LHS, we get x = 4.

Q 40.

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-3

Q 41.

Two numbers differ by 40. When each number is increased by 8, the bigger becomes thrice the lesser number. If one number is x, then the other number is (40 – x).

Q 42.

frac { 2x-1 }{ 5 } =frac { 3x+1 }{ 3 }

Q 43.

 frac { 2y-3 }{ 4 } -frac { 3y-5 }{ 2 } =y+frac { 3 }{ 4 }

Q 44.

 frac { 3x+2 }{ 2x-3 } =-frac { 3 }{ 4 }

Q 45.

 m-frac { m-1 }{ 2 } =1-frac { m-2 }{ 3 }

Q 46.

The sum of three consecutive even natural numbers is 48. Find the greatest of these numbers.

Q 47.

Two equal sides of a triangle are each 4 m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55 m.

Q 48.

The sum of four consecutive integers is 266. What are the integers?

Q 49.

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 50.

If numerator is 2 less than denominator of a rational number and when 1 is subtracted from numerator and denominator both, the rational number in its simplest form is 1/2. What is the rational number?