Question

How do you solve $2x + 12 - 7x = - 2?$

Answer 1

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.