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**Hint:**The equation given in the above question is a linear equation in one variable, that is x. The question says that we have to solve the given equation in x. In other words, we have to find the values of x which will satisfy the given equation. Try to find the value of x by performing some mathematical operations.

**Complete step-by-step solution:**

The given equation says that $5x+1=21$.

Let us analyse the above linear equation in x and try to simplify it and find the value of x.

The first thing that we can do here is to club the terms that are multiple of x on one side of the equation (say the left hand side) and then club the constant terms on the right hand side of the equation.

If we do the above process, then we get that the above equation changes to $5x=21-1$

If we simplify the equation, then we get that $5x=20$ …. (i)

Next, we can divide the equation (i) by 5 (on both the sides) so that the coefficient of x becomes 1.

With this, we get that $\dfrac{5x}{5}=\dfrac{20}{5}$

$\Rightarrow x=4$.

This means that the value of x that satisfies the given equation is 4.

Hence, the solution of the equation $5x+1=21$ is $x=4$

**Note:**There are many ways in which we can solve this question. We can also divide the equation by 5 and then club the x terms on one side and the constant terms on the other. However, students must note that the number of solutions to a given equation in one variable is always less than or equal to the degree of the polynomial in the given equation.

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