Question

How do you solve $3x+4=1$ ?

Answer 1

Hint: For getting the solution of the given question, we will use the method of the inverse identity of addition and inverse identity of the multiplication. So, in the question first of all we will use the inverse identity of addition and after that we will get the simplified value. Then, we will use the method of inverse of multiplication. Again we will simplify the equation. Then we will get the final answer.

Complete step by step solution:
Since, we have the equation of the given question that is $3x+4=1$, where we can use the inverse method of addition and multiplication respectively.
$\Rightarrow 3x+4=1$
Since, we have a number in addition that is $4$ whose inverse identity of addition is $-4$ . So , we use this inverse identity of addition in the above equation both side as:
$\Rightarrow 3x+4-4=1-4$
Now, we will simplify the above equation where $4$ will be eliminated by $-4$ and we will get the $-3$ after using subtraction method for $1$ and $4$ as:
$\Rightarrow 3x=-3$
Since, we have the above equation as $3x=-3$ . So, we will use the method of inverse identity of multiplication. Here, we will use number $3$ as inverse identity of multiplication and will divide by this number in the above equation both sides as:
$\Rightarrow \dfrac{3x}{3}=\dfrac{-3}{3}$
Now, $3$ will eliminate $3$on left hand side and $3$ will also eliminate $-3$ on right hand side as:
$\Rightarrow x=-1$
Hence, we got the solution $x=-1$ for the given question $3x+4=1$ .

Note: Since, we got the value of $x$ as $x=-1$ . Now, we will put the value of $x$ in the given question as:
$\Rightarrow 3x+4=1$
$\Rightarrow 3\left( -1 \right)+4=1$
$\Rightarrow 3\times -1+4=1$
$\Rightarrow -3+4=1$
Now, we get the final value after subtraction as:
 $\Rightarrow 1=1$
Since, \[\text{LHS}=\text{RHS}\] . Hence, the solution is correct.