Question

How do you solve\[9 - 2x = 35?\]

Answer 1

Hint: This question involves the arithmetic operations of addition/ subtraction/ multiplication/ division. We need to know how to separate the \[x\]term from constant terms. We would find the value of\[x\]from the given equation. Also, we need to know the arithmetic operations involved with different sign terms.

Complete step-by-step answer:
The given equation in the question is shown below,
\[9 - 2x = 35 \to \left( 1 \right)\]
To solve the given equation we would separate the\[x\]term to one side of the equation and constant terms to another side of the equation. For that we move\[ - 2x\]from the left-hand side to the right-hand side of the equation so, it will convert into\[2x\] as shown below,
\[9 = 35 + 2x \to \left( 2 \right)\]
Next, we move the term\[35\] from the right-hand side to the left-hand side of the above equation. So, we get
\[9 - 35 = 2x\]
By solving the above equation we get,
\[ - 26 = 2x\]
Next, we move the term\[2\]from the right-hand side to the left-hand side of the above equation, we get
\[
  \dfrac{{ - 26}}{2} = x \\
   - 13 = x \\
 \]
So, the final answer is,
\[x = - 13\]

Note: The given question describes the operation of addition/ subtraction/ multiplication/ division. Note that when we move one term from LHS to RHS or RHS to LHS, the arithmetic operations can be modified as follows,
The multiplication process will be converted into the division process.
The division process will be converted into the multiplication process.
The addition process will be converted into the subtraction process.
The subtraction process will be converted into the addition process.

Also, note the following when we multiplying different sign terms,
i) \[\left( - \right) \times \left( - \right) = \left( + \right)\]
ii) \[\left( + \right) \times \left( + \right) = \left( + \right)\]
iii) \[\left( + \right) \times \left( - \right) = \left( - \right)\]