Question

How do you solve the linear equation $3x+4=2x-1$?

Answer 1

Hint: We are given a simple equation in one variable and to solve this equation further and find the value of that variable, we must rearrange the terms. Right now in the given equation, two terms of the same variable are given and two constant terms are given on the left-hand side and right-hand side of the equation. We shall transpose these terms to find the value of x-variable.

Complete step-by-step solution:
We know that according to basic mathematics, the mathematical operations like addition and subtraction can be performed only on the like terms. This means only similar terms of the same variable or unit can be added or subtracted.
Here, we are given four terms in this equation, $3x+4=2x-1$, where two of them are of x-variable with different coefficients and the rest two are constant terms. Thus, we shall bring these like terms together by transposing in the equation and add or subtract them accordingly.
Grouping the x-variable terms in the left-hand side and the constant terms on the right-hand side of equation, we get
$\Rightarrow 3x-2x=-1-4$
Now, subtracting and adding the terms respectively, we get
$\Rightarrow x=-5$
 $\therefore x=-5$
Therefore, we get $x=-5$ on solving $3x+4=2x-1$.

Note: We often tend to make mistakes while changing the sign of the terms while transposing them. Whenever we transpose terms from the left-hand side to the right-hand side of an equation or vice-versa, the sign of the term being transposed changes. This implies that the positive term becomes negative and the negative term becomes positive.