Question

How do you solve for $x$ in $x\left( {1 + y} \right) = z$?

Answer 1

Hint: Here we need to solve the given literal equation. For that, we will isolate the term of which we want the value. To isolate the term, we will divide both sides of the equation by the term with which the required term is multiplied. Then we will perform certain mathematical operations to get the value.

Complete step by step solution:
Here we need to solve the given literal equation and the given literal equation is $x\left( {1 + y} \right) = z$ and we need to find the value of $x$ here.
For that, we have to isolate the term $x$ in the literal equation.
 To isolate the term, we will divide both sides of the literal equation by the term with which the required term is multiplied.
We can see that the term $x$ is multiplied with the terms which are inside the parentheses i.e. $\left( {1 + y} \right)$
So, we have to divide both sides of the literal equation by $\left( {1 + y} \right)$ to isolate the term $x$.
On dividing both sides by $\left( {1 + y} \right)$, we get
$ \Rightarrow \dfrac{{x\left( {1 + y} \right)}}{{\left( {1 + y} \right)}} = \dfrac{z}{{\left( {1 + y} \right)}}$
On further simplifying the terms, we get
$ \Rightarrow x = \dfrac{z}{{\left( {1 + y} \right)}}$

Therefore, the required value of the term is equal to $\dfrac{z}{{\left( {1 + y} \right)}}$.

Hence, this is the required solution to the given equation.

Note:
Here we have obtained the solution of the given literal equation i.e. we have obtained the value of $x$ here. Here literal equations are defined as the equations which consist of the letters or in other words we can define literal equations as the equations which consist of more than one variable. We have also used various mathematical operations to solve the given algebraic equation. So we need to remember that when we multiply two negative numbers together then the resultant value will be a positive number.