How do you solve, \[\mathbf{7}\left( \mathbf{4x}+\mathbf{2} \right)+\mathbf{3}=-\mathbf{67}\]?

Hint: For determining the value of \[x\] multiply \[\left( 4x+2 \right)\] with \[7\] in left side of equation then separate the like terms at one side, after solving the expression by using BODMAS determine the value of unknown quantity \[x\].

Complete step by step solution:
As per data given in the question,
As we have to solve the expression,
Let’s multiply the term \[\left( 4x+2 \right)\] by \[7\]
We will get,
\[28x+14+3=-67\]
Now simplifying the like terms,
We will get,
\[28x+17=-67\]
Now separating the like terms at one side, for that shifting \[17\] from left side of equation to the right side of equation,
As \[17\] is in addition with \[28x\] so when it will be separated to right side it comes in subtraction,
Hence, we will get,
\[28x+17=-67\]
Now simplifying the like terms of right side,
We will get,
\[28x=-84\]
As here, 28 is in multiplication with \[x\] so when it will be shifted to right side of equation it will comes in division,
Hence, we will get,
\[x=-84/28=-3\]
Hence, value of \[x\] in above expression will be \[-3\]
So, when we put \[x=-3\] in the above expression then the value obtained by solving the left side of the equation will be equal to the value obtained by the right side of the equation.

Note: While transferring the digits or constants or any variables or numbers from left hand side to right hand side, make sure you are reversing its symbol.
For any mathematical operation, always follow only the BODMAS rule.