Answer :
Certainly! Let's solve each part one by one to check whether the given values are solutions to the respective equations.
### Part (i)
Equation: \( x + 5 = 3 \)
Given \( x = 2 \).
Substitute \( x = 2 \) into the equation:
[tex]\[ 2 + 5 = 7 \][/tex]
The right-hand side of the equation is 3, but the left-hand side, after substitution, gives 7.
Since \( 7 \neq 3 \), \( x = 2 \) is not a solution to \( x + 5 = 3 \).
### Part (ii)
Equation: \( 8n + 5 = 21 \)
Given \( n = 2 \).
Substitute \( n = 2 \) into the equation:
[tex]\[ 8(2) + 5 = 16 + 5 = 21 \][/tex]
Both sides of the equation are equal to 21.
Since \( 21 = 21 \), \( n = 2 \) is a solution to \( 8n + 5 = 21 \).
### Part (iii)
Equation: \( 4x + 3 = 5 \)
Given \( x = -2 \).
Substitute \( x = -2 \) into the equation:
[tex]\[ 4(-2) + 3 = -8 + 3 = -5 \][/tex]
The right-hand side of the equation is 5, but the left-hand side, after substitution, gives -5.
Since \( -5 \neq 5 \), \( x = -2 \) is not a solution to \( 4x + 3 = 5 \).
### Part (iv)
Equation: \( 5p + 3 = 7 \)
Given \( p = -3 \).
Substitute \( p = -3 \) into the equation:
[tex]\[ 5(-3) + 3 = -15 + 3 = -12 \][/tex]
The right-hand side of the equation is 7, but the left-hand side, after substitution, gives -12.
Since \( -12 \neq 7 \), \( p = -3 \) is not a solution to \( 5p + 3 = 7 \).
### Part (v)
Equation: \( 4p - 3 = 13 \)
Given \( p = 1 \).
Substitute \( p = 1 \) into the equation:
[tex]\[ 4(1) - 3 = 4 - 3 = 1 \][/tex]
The right-hand side of the equation is 13, but the left-hand side, after substitution, gives 1.
Since \( 1 \neq 13 \), \( p = 1 \) is not a solution to \( 4p - 3 = 13 \).
### Part (vi)
Equation: \( -3p - 2 = 10 \)
Given \( p = -4 \).
Substitute \( p = -4 \) into the equation:
[tex]\[ -3(-4) - 2 = 12 - 2 = 10 \][/tex]
Both sides of the equation are equal to 10.
Since \( 10 = 10 \), \( p = -4 \) is a solution to \( -3p - 2 = 10 \).
### Summary
To summarize, the given values are solutions to the equations as follows:
(i) \( x = 2 \): Not a solution
(ii) \( n = 2 \): Solution
(iii) \( x = -2 \): Not a solution
(iv) \( p = -3 \): Not a solution
(v) \( p = 1 \): Not a solution
(vi) [tex]\( p = -4 \)[/tex]: Solution
### Part (i)
Equation: \( x + 5 = 3 \)
Given \( x = 2 \).
Substitute \( x = 2 \) into the equation:
[tex]\[ 2 + 5 = 7 \][/tex]
The right-hand side of the equation is 3, but the left-hand side, after substitution, gives 7.
Since \( 7 \neq 3 \), \( x = 2 \) is not a solution to \( x + 5 = 3 \).
### Part (ii)
Equation: \( 8n + 5 = 21 \)
Given \( n = 2 \).
Substitute \( n = 2 \) into the equation:
[tex]\[ 8(2) + 5 = 16 + 5 = 21 \][/tex]
Both sides of the equation are equal to 21.
Since \( 21 = 21 \), \( n = 2 \) is a solution to \( 8n + 5 = 21 \).
### Part (iii)
Equation: \( 4x + 3 = 5 \)
Given \( x = -2 \).
Substitute \( x = -2 \) into the equation:
[tex]\[ 4(-2) + 3 = -8 + 3 = -5 \][/tex]
The right-hand side of the equation is 5, but the left-hand side, after substitution, gives -5.
Since \( -5 \neq 5 \), \( x = -2 \) is not a solution to \( 4x + 3 = 5 \).
### Part (iv)
Equation: \( 5p + 3 = 7 \)
Given \( p = -3 \).
Substitute \( p = -3 \) into the equation:
[tex]\[ 5(-3) + 3 = -15 + 3 = -12 \][/tex]
The right-hand side of the equation is 7, but the left-hand side, after substitution, gives -12.
Since \( -12 \neq 7 \), \( p = -3 \) is not a solution to \( 5p + 3 = 7 \).
### Part (v)
Equation: \( 4p - 3 = 13 \)
Given \( p = 1 \).
Substitute \( p = 1 \) into the equation:
[tex]\[ 4(1) - 3 = 4 - 3 = 1 \][/tex]
The right-hand side of the equation is 13, but the left-hand side, after substitution, gives 1.
Since \( 1 \neq 13 \), \( p = 1 \) is not a solution to \( 4p - 3 = 13 \).
### Part (vi)
Equation: \( -3p - 2 = 10 \)
Given \( p = -4 \).
Substitute \( p = -4 \) into the equation:
[tex]\[ -3(-4) - 2 = 12 - 2 = 10 \][/tex]
Both sides of the equation are equal to 10.
Since \( 10 = 10 \), \( p = -4 \) is a solution to \( -3p - 2 = 10 \).
### Summary
To summarize, the given values are solutions to the equations as follows:
(i) \( x = 2 \): Not a solution
(ii) \( n = 2 \): Solution
(iii) \( x = -2 \): Not a solution
(iv) \( p = -3 \): Not a solution
(v) \( p = 1 \): Not a solution
(vi) [tex]\( p = -4 \)[/tex]: Solution
