Question

How do you solve $2(x + 1) = 2x + 2$ ?

Answer 1

Hint:The mathematical equations that are a combination of both numerical values and alphabets are called algebraic expressions. Thus, the equation given in the equation is an algebraic equation. In simple words, algebra is known as the representation of numbers by alphabets in a formula or equation involving mathematical operations. $2x$ and $2(x + 1)$ represent the multiplication of 2 and x, and 2 and x+1 respectively and they both are given to be equal to each other so simplifying this equation, we can find the value of x.

Complete step by step answer:
Let us take the left-hand side of the equation and solve it –

We have to simplify $2(x + 1)$ 2 multiplied with x is equal to 2x and 2 multiply with 1 is equal to 2, now they both are in addition,
so $2(x + 1) = 2x + 2$

Now, comparing this equation with the right-hand side, we get –
$
2x + 2 = 2x + 2 \\
\Rightarrow 2x = 2x \\
\Rightarrow x = x \\
$

As we have got the result as $x = x$ , it means that x is equal to any real number or x lies in the
interval $( - \infty ,\infty )$ .

Note:The given equation is already in the simplified form, so it cannot be simplified further that’s why we apply distributive property on the equation, according to which when one quantity is in multiplication with two quantities written in the parenthesis, it is equal to the sum of that quantity multiplied with each quantity in the bracket individually, that is, $c(a + b) = ac + bc$ . As the “2” term is in multiplication with both the terms, we remove the parentheses and multiply it individually with both the terms and then apply the given arithmetic operation.