Question

How many solutions exist for the equation $3(x + 10) + 6 = 3(x + 12)$ ?

Answer 1

Hint: Here, we have to find the number of solutions for the equation $3(x + 10) + 6 = 3(x + 12)$. In order to find the number of solutions we solve the given equation and find the value of $x$ by doing various operations. The given expression is a linear equation in one variable.

Complete step by step answer:
Here, we have to find the value of the number of solutions for the given linear equation. So, we have to find the value of $x$ in the given equation. The given equation is a linear equation in one variable. Linear equations are the equations when we have a variable of maximum one order or degree in an equation. Here, the degree of $x$ is $1$ hence, the above equation is a linear equation in one variable.

We have $3(x + 10) + 6 = 3(x + 12)$
Solving both the sides of the equation. We get,
$ \Rightarrow 3x + 30 + 6 = 3x + 36$
Adding constant terms in the left side of the equation. We get,
$ \Rightarrow 3x + 36 = 3x + 36$
Taking $x$ terms one side and constant terms to another side. We get,
$ \Rightarrow 3x - 3x = 36 - 36$
On solving we get,
$ \Rightarrow 0 \cdot x = 0$
So, for all the values of $x$ in Real number the equation is satisfied.Therefore, there exist an infinite number of solutions.

Hence, the equation $3(x + 10) + 6 = 3(x + 12)$ has an infinite number of solutions for $x$.

Note: In an equation the total number of variables determines the number of solutions it will produce and on the basis of this the solution can be grouped into three types such as unique solution which has only one solution, no solution that means have no solutions and infinitely number of solutions means which has many solutions.