Chapter 4: Linear Equations in One Variable

Solution:-

False.

Given, 2x = 4 – x

Transposing –x to LHS it becomes x

2x + x = 4

3x = 4

X = 3/4

Solution:-

False.

Given, (15/8) – 7x = 9

Transposing 15/8 to RHS it becomes – (15/8)

– 7x = 9 – (15/8)

Solution:-

False.

Given, (x/3) + 1 = (7/15)

Transposing 1 to RHS it becomes – 1

(x/3) = (7/15) – 1

(x/3) = (7 – 15)/15

(x/3) = -8/15

Solution:-

True.

Given, 6x = 18

Multiplying both LHS and RHS by 3, we get

6x × 3 = 18 × 3

18x = 54

Solution:-

False.

Given, x/11 = 15

Multiplying both LHS and RHS by 11, we get

(x/11) × 11 = 15 × 11

X = 165

Solution:-

False.

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

Solution:-

False.

From the question,

The sum of two consecutive numbers is 93

Two consecutive number are = x and 93 – x

Then, sum of two consecutive numbers = x + (93 – x) = 93

X + 93 – x = 93

Transposing 93 to RHS it becomes – 93

x – x = 93 -93

0 = 0

Solution:-

False.

From the question it is given that,

One number = x

Other number = 40 –x

Let us assume (40 – x) > x

So, 40 – x + 8 = 3 (x + 8)

48 – x = 3x + 24

– x – 3x = 24 -48

– 4x = -24

X = -24 × (-1/4)

X = 6

∴One number is x = 6

Other number is = 40 – x

= 40 – 6

= 34

Difference between numbers = 34 – 6 = 28

Solve the following:

Solution:-

We have,

((3x – 8)/2x) = 1

By cross multiplication, we get

(3x – 8) = 2x

Transposing -8 to RHS it becomes 8 and 2x to LHS it becomes – 2x

3x – 2x = 8

x = 8

Solution:-

We have,

(5x/(2x – 1)) = 2

By cross multiplication, we get

5x = 2 × (2x – 1)

5x = 4x – 2

Transposing 4x to LHS, it becomes – 4x

5x – 4x = -2

x = -2