Question

Ans me 5 , 6 and 7 ​

Answer 1

1) |8-10|

= |-2| = 2

2)

$| \frac{7 - x}{2} | = 6 \\ \\ 7 - x = 6 \times 2 \\ \\ 7 - x = 12 \\ \\ - x = 12 - 7 = 5 \\ \\ x = - 5$

The required value of x = -5

3)

$29. \: { \bar{5}{ \bar{6}{ \bar{8}}}}$

Let it = x

X = 29.568568... –––(Eq.1)

Then ,

Multiply both sides by 1000

1000 x = 29568.568... ---(Eq.2)

Subtracting EQ 1 from EQ 2 :

999 x = 29539

So , x = 29539/999

The required rational number = 29539/999

Answer 2

Ques.5 ) | 8 - 10 |

Solution : | 8 - 10 | ⇒| - 2 |

Here, | | refers to absolute symbol that changes negative sign into positive sign.

⇒ | -2 | = + 2

Answer : 2

Ques.6 ) | ( 7 - x )/2 | = 6

Solution :

Case 1. | ( 7 - x )/2 | = 6

⇒( 7 - x )/2 = 6

⇒7 - x = 6 × 2

⇒- x = 12 - 7

⇒ x = - 5

Why do | | had made no change here? Because,

| [ { 7 - ( - 5 )} / 2 ] | = | 12 / 2| = | 6 |

Since | | has no effect on positive numbers, thats why | | will not efffect solution here.

Case 2. | ( x - 7 )/2 | = 6

x - 7 = 12

x = 19

Here, | ( 19 - 7 ) / 2 | = 6

| 12 / 2 | = | 6 | = 6

Answer : -5 and 19

Ques.7 ) Represent 29.568568.... in p/q form.

Solution : Let x = 29.568568....... _(i)

No. of digits under bar are 3 so.multiply 1000 from x.

1000x = 29568.568568...... _(ii)

By doing (ii) - (i),

999x = 29568.568568 - 29.568568

x = 29539/999

Answer : 29539/999