The given equations in statement form are as follows:
The difference of m and 7 is 3.

When, n = 2
then 7n + 5 = 7 \(\times\) 2 + 5 = 14 + 5
= 19
So, n = 2 is the solution of the given equation.

Given equation, 6x - 4 = 22
We will try to get x on LHS of this equation
∴ 6x - 4 + 4 = 22 + 4 ⇒ 6 x= 26          [adding 4 to both sides]
Now, on dividing both sides by 6, we get
\(\frac { 6x }{ 6 } =\frac { 26 }{ 6 } \)  or \(x=\frac { 26 }{ 6 } =\frac { 13 }{ 3 } \)           [dividing numerator and denominator by 2]
Thus, x =\(\frac { 13 }{ 3 } \) is the solution.

Let Laxmi 's age be x yr, then 4 times of Laxrni's age be 4x.
\(\therefore\) Laxmi's father age = 3x + 4, but Laxmi's father is 49 yr.
Therefore, we get the equation, 3x + 4 = 49
To solve this equation, transposing 4 from LHS to RHS, we get 3x = 49 - 4  \(\Rightarrow\)  3x = 45
On dividing both sides by 3, we get = 15
Hence, Laxmi's age is 15 yr.

Let the number be x.
Three-fourths of the number = \(\frac{3}{4}x\)
According to the question,
On adding 3 to it, we get 2l.
i.e.   \(\frac{3}{4}x+3=21\)
which is the required equation.
Now, to solve this equation, transposing (+3) from LHS to RHS, we get
       \(\frac{3}{4}x=21-3\quad \Rightarrow \frac{3}{4}x=18\)
On multiplying both sides by 4, we get
       \(\frac{3}{4}x\times 4=18\times 4\Rightarrow 3x=72\)
Again, dividing both sides by 3, we get
       \(\frac{3x}{3}=\frac{72}{3}\quad \Rightarrow x=24\)
Hence, the required number is 24.

Given equation is 5P + 2 = 17.
When P = 0, then LHS = 5\(\times\)0 + 2 = 0 + 2 = 2
and    RHS = 17
∴ LHS ≠ RHS
When p = 1, then LHS = 5\(\times\)1+ 2 = 5 + 2 = 7
and RHS = 17
∴  LHS ≠ RHS
When p = 2, then LHS = 5\(\times\)2 + 2 = 10 + 2 = 12
and  RHS =17
∴  LHS ≠ RHS
When p = 3, then LHS = 5\(\times\)3 + 2 = 15 + 2 = 17
∴  LHS = RHS
So, p = 3 is the solution of the given equation.

Let x be the age of Amit.
So, age of Sohan Lal, the father of Amit = 4x yr
If the difference of their ages is 27 yr.
Then, 4x- x = 27 \(\Rightarrow\) 3x = 27 \(\Rightarrow x=\frac{27}{3}=9\)
Hence, age of Amit is 9 yr.

Given, \(x-\frac{1}{2}=\frac{-1}{2}\)
\(\frac{2x-1}{2}=\frac{1}{2}\Rightarrow \) 2x - 1 = -1  \(\Rightarrow\)  2x = 0   \(\Rightarrow\) x = 0
So, if \(x-\frac{1}{2}=\frac{-1}{2}\) then x = 0.

Any term of an equation may be transposed from one side of the equation to the other side of the equation by changing the sign of the term,
e.g. 2x + 4 = 2
If 4 is transposed. then
2x = 2 - 4 [sign changed]

Given \(\frac{x}{2}=6 \Rightarrow\) = x = 6 x 2 = 12
\(\therefore\)  12 - (-3) = 12 + 3 = 15
So, x - (-3) = 15, When \(\frac{x}{2}=6\)