# Linear Equations in One Variable

### Question:

The solutoni of the equation ax + b = 0 is

### Linear Equations in One Variable

#### Q 1.

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

#### Q 2.

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 3.

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

#### Q 4.

After 12 years, Kanwar shall be 3 times as old as he was 4 years ago. Find his present age.

#### Q 5.

The solutoni of the equation ax + b = 0 is

#### Q 6.

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 7.

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

#### Q 8.

Convert the statement ‘adding 15 to 4 times x is 39’ into an equation.

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

#### Q 10.

$frac { x+1 }{ 4 } =frac { x-2 }{ 3 }$

#### Q 11.

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

#### Q 12.

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 13.

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 14.

$frac { 2x-3 }{ 4x+5 } =frac { 1 }{ 3 }$

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

#### Q 16.

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 17.

The solution of the equation 2y = 5y-$frac { 18 }{ 5 }$ is————.

#### Q 18.

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

#### Q 19.

On subtracting 8 from x, the result is 2. The value of x is——–.

#### Q 20.

$frac { x }{ 5 } =frac { x-1 }{ 6 }$

#### Q 21.

$frac { 3t+5 }{ 4 } -1=frac { 4t-3 }{ 5 }$

#### Q 22.

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 23.

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

#### Q 24.

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 25.

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 26.

The share of A when Rs 25 are divided between A and B, so that A gets Rs 8 more than B, is——–.

#### Q 27.

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

#### Q 28.

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

#### Q 29.

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

#### Q 31.

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

#### Q 32.

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

#### Q 33.

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

#### Q 34.

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

#### Q 35.

Divide 54 into two parts, such that one part is 2/7 of the other.

#### Q 36.

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 37.

Denominator of a number is 4 less than its numerator. If 6 is added to the numerator, it becomes thrice the denominator. Find the fraction.

#### Q 38.

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 39.

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

#### Q 40.

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

#### Q 41.

3 years ago, the age of boy was y years. His age 2 years ago was (y â€” 2) years.

#### Q 42.

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 43.

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 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 46.

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

#### Q 47.

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

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

#### Q 50.

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