Question

How do you solve $9x + 1 = 7 + 3x$ ?

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. $9x$ and $3x$ represent the multiplication of 9 and x, and 3 and x respectively and they both are on the opposite sides of the equation, so for solving the given equation, we will move all the terms containing x on one side and constant terms on the other side.
Using this approach, we can find the value of x.

Complete step by step answer:
Rearranging the given equation, we get –
$
9x + 1 = 7 + 3x \\
\Rightarrow 9x - 3x = 7 - 1 \\
\Rightarrow x(9 - 3) = 6 \\
\Rightarrow 6x = 6 \\
\Rightarrow x = \dfrac{6}{6} \\
\Rightarrow x = 1 \\
$
Hence, when $9x + 1 = 7 + 3x$ , we get $x = 1$ .

Note:
The given equation is already in the simplified form as it involves a degree of 1, so it cannot be simplified further so we just rearrange the given equation.
When we bring the terms containing x to the left-hand side, we apply distributive property, 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 and vice versa, that is, $c(a + b) = ac + bc$ or $ac + bc = c(a + b)$ .
As the “x” term is in multiplication with both the numbers, we take it as common and put the rest of the terms in the parenthesis and apply the given arithmetic operation in
the parenthesis.