Question

How do you solve $13 - 4x = 1 - x$?

Answer 1

Hint: Here we need to solve the given algebraic equation i.e. we need to find the value of the variable used in the given algebraic equation. We will use different mathematical operations here to solve it. First, we will subtract the number from both sides of the equation and then we will divide both sides by the number which is multiplied with the variable and after simplification, we will get the required value of the variable used in the given algebraic equation and hence, the required solution of the given algebraic equation.

Complete step by step solution:
We need to find the value of the variable used in the given algebraic equation.
$ 13 - 4x = 1 - x$
Now, we will add the term $x$ to both sides.
$ \Rightarrow 13 - 4x + x = 1 - x + x$
On further simplification, we get
$ \Rightarrow 13 - 3x = 1$
We will first subtract 13 from both sides of the algebraic equation.
$ \Rightarrow 13 - 3x - 13 = 1 - 13$
On further simplification, we get
$ \Rightarrow - 3x = - 12$
Now, we will divide both sides of the algebraic equation by -3.
$ \Rightarrow \dfrac{{ - 3x}}{{ - 3}} = \dfrac{{ - 12}}{{ - 3}}$
On further simplifying the terms, we get
$ \Rightarrow x = 4$

Therefore, the value of the required variable used in the algebraic equation is equal to 4 and hence, this is the required solution of the given algebraic equation.

Note:
Here we have obtained the required value of the variable used in the algebraic equation. The algebraic equation used in the question is a linear algebraic equation because the degree of the equation is 1. 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.