Question

(i) Find the least positive value of x such that 67+x=1(mod 4)
(ii) Solve 5x = 4(mod 6)​

Answer 1

Answer:

see below

Step-by-step explanation:

The Modulus is the remainder of the euclidean division of one number by another. % is called the modulo operation.

1 mod 4 = 1 % 4 = 1

Therefore

67+x=1(mod 4)

67+x= 1

x=1 - 67

x= -66

(ii) Solve 5x = 4(mod 6)​

4 mod 6 = 4 % 6 = 4

Therefore

5x= 4

x= 4/5

Answer 2

Answer:

(i) The least positive value of x = - 63

(ii) The least positive value of x = 4.8

Step-by-step explanation:

Given as :

(i) The linear equation is  67 + x = 1 × $\left | 4 \right |$

The mode sign is for once + ve value and other - ve value

For positive sign

The equation can be written

67 + x = 1 × ( + 4 )

Or, 67 + x = 4

Or, x = 4 - 67

∴   x = - 63

For negative sign

The equation can be written

67 + x = 1 × ( - 4 )

Or, 67 + x = - 4

Or, x = - 4 - 67

∴   x = - 71

Hence, The least positive value of x = - 63   . Answer

(ii) The linear equation is  5 x = 4 × $\left | 6 \right |$

The mode sign is for once + ve value and other - ve value

For positive sign

The equation can be written

5 x = 4 × ( + 6 )

Or, 5 x = 24

Or, x = $\dfrac{24}{5}$

∴   x =  4.8

For negative sign

The equation can be written

5 x = 4 × ( - 6 )

Or, 5 x = - 24

Or, x = $\dfrac{-24}{5}$

∴   x = - 4.8

Hence, The least positive value of x = 4.8    . Answer