Question

Solve the following equation and verify your answer.$2(x - 1) = x + 2$

Answer 1

Hint: To solve this type of linear equation we will take variable terms to one side and constants to the other side then we will apply different mathematical operations to get the required solution.

Complete step by step answer:
Given that the equation $2(x - 1) = x + 2$ and then we need to find the value of the unknown variable $x$, we will make use of the basic mathematical operations to simplify further.
By the multiplication operation, we get $2(x - 1) = x + 2$
$ \Rightarrow 2x - 2 = x + 2$
now Turing the variables on the left-hand side and also the numbers on the right-hand side we get $2x - 2 = x + 2 $
$\Rightarrow 2x - x = 2 + 2$ while changing the values on the equals to, the sign of the values or the numbers will change.
Now by the addition and subtraction operation, we get $x = 4$ (for example: $2x - x = x(2 - 1) = x(1) = x$ which is also applicable for the variables)
Hence, we get $x = 4$ as the answer and if we substitute the answer in the given question then we get $2(x - 1) = x + 2$
$ \Rightarrow 2(4 - 1) = 4 + 2$
Again, by the addition, multiplication, and subtraction we get \[2(x - 1) = x + 2 \]
\[\Rightarrow 2(4 - 1) = 4 + 2 \]
\[\Rightarrow 6 = 6\] , and hence the values on both sides are the same when we substitute the variable found value. Or we can also say that, if both sides are equal to some value of the given variable, and hence which is the correct answer for the unknown variable.
Hence $x = 4$ is the correct answer.

Note:
There are three methods to solve linear equations in one variable.
1. Trial and Error.
2. Inverse operations.
3. Transposition Method.