Question

How do you solve $3x + 4 = 22$ ?

Answer 1

Hint: The equation that we need to solve here is a linear equation in one variable. To solve this equation, we need to simplify it by keeping the required variable terms on the left and the remaining terms on right and then evaluate it further. We add or subtract the same degree terms here during evaluation. Since it is a degree $1$ equation we get only one solution for $x$.

Complete step by step solution:
The given equation $3x + 4 = 22$ , is a linear equation in one variable.
A linear equation means that the degree of the equation is $1$ . In other words, we say that the highest power of the variable in the equation is $1$ . A linear equation represents a straight line.
Now put the same degree terms on one side.
The degree of $3x\;$ is $1$ since the power of the variable $x$ is $1$ .
The degree of $4,22\;$ is $0$ since the power of the variable $x$ is $0$ .
For rearranging, we subtract $4$ on both sides of the equation.
We get,
$ \Rightarrow 3x + 4 - 4 = 22 - 4$
$ \Rightarrow 3x = 18$
Now must find the solution for the variable $x$ .
It is associated with the constant $3$ .So, we now divide with $3$ on both sides of the equation to get the variable $x$ alone.
$ \Rightarrow \dfrac{{3x}}{3} = \dfrac{{18}}{3}$
Factorize the numerator on the RHS.
$ \Rightarrow \dfrac{{3x}}{3} = \dfrac{{2 \times 3 \times 3}}{3}$
Now evaluate further.
$ \Rightarrow x = 2 \times 3$
$ \Rightarrow x = 6$

Hence the solution for our given equation is $x = 6$.

Note: For Linear equations in one variable we get only one solution since the degree of the equation is $1$ . We can always crosscheck for our answer by substituting back in the given linear equation. Here we substitute $x = 6$ in the equation.
$ \Rightarrow 3x + 4 = 22$
$ \Rightarrow 3(6) + 4 = 22$
On solving further, we get,
$ \Rightarrow 18 + 4 = 22$
$ \Rightarrow 22 = 22$
LHS=RHS;
Hence our solution is correct.