Question

How do you solve \[2x + 12 - 7x = - 2?\]

Answer 1

Hint:This question involves the operation of addition/ subtraction/ multiplication/ division. We need to know how to separate the\[x\]term and constant terms from the given equation to make an easy calculation. Also, we need to know the multiplication process between different sign terms. The final answer would be a value of \[x\].

Complete step by step solution:
The given equation in the question is shown below,
\[2x + 12 - 7x = - 2 \to \left( 1 \right)\]
To solve the above equation we would separate the\[x\]term into one side and the constant term into another side of the above equation. So, we get
\[\left( 1 \right) \to 2x + 12 - 7x = - 2\]
The above equation can also be written as,
\[2x + 12 - 7x + 2 = 0\]
(\[ - 2\]can be converted into\[2\] when we move it from right side to left side of the equation)
\[\left( {2x - 7x} \right) + 12 + 2 = 0 \to \left( 2 \right)\]
We know that,
\[
12 + 2 = 14 \\
2x - 7x = 5x \\
\]
By substituting these values in the equation \[\left( 2 \right)\], we get
\[\left( 2 \right) \to \left( {2x - 7x} \right) + 12 + 2 = 0\]
\[ - 5x + 14 = 0\]
Let’s separate the\[x\]term and constant term in the above equation, so we get
\[
- 5x = - 14 \\
x = \dfrac{{ - 14}}{{ - 5}} \\
\]
\[x = \dfrac{{14}}{5}\]
So, the final answer is,
\[x = \dfrac{{14}}{5}\]

Note: The given question involves the operation of addition/ subtraction/ multiplication/ division. For solving this type of question we have to separate the \[x\] and constant term from the given equation. When we multiply/ divide the different sign terms we have to remember the following things,
1) When a negative number is multiplied/ divided with a negative number the final answer
would be a positive number.
2) When a positive number is multiplied/ divided with a positive number the final answer
would be a positive number.
3) When a negative number is multiplied/ divided with a positive number the final answer
would be a negative number.