Question

How do you solve \[4x - 24 = - 5x + 12\]?

Answer 1

Hint: The given equation is a linear equation in one variable $x$. A linear equation is an equation where the degree or highest power of the variable is 1. Solving the equation means finding the value of $x$ for which the equality holds true for the given equation. We will get only one value of $x$ as the solution of a linear equation.

Complete step by step solution:
For solving the equation we have to find the value of $x$ for which the equality holds true, i.e. LHS=RHS.
We first shift all the terms to the LHS such that we have only the term $0$ in the RHS.
For this we first add both sides by $5x$, we get,
$
  4x - 24 + 5x = - 5x + 12 + 5x \\
   \Rightarrow 4x + 5x - 24 = 12 \\
$
Now we subtract $12$ on both sides, we get,
$
  4x + 5x - 24 - 12 = 12 - 12 \\
   \Rightarrow 4x + 5x - 36 = 0 \\
   \Rightarrow 9x - 36 = 0 \\
$
We can clearly see that the above equation is a linear equation in one variable $x$ with general form $ax + b = 0$.
Now we try to write the LHS in terms of the variable $x$ in its simplest form and shift all other terms to the RHS.
For this we first add $36$ on both sides,
$
  9x - 36 + 36 = 0 + 36 \\
   \Rightarrow 9x = 36 \\
 $
Then we divide on both sides by $9$, we get,
\[
   \Rightarrow \dfrac{{9x}}{9} = \dfrac{{36}}{9} \\
   \Rightarrow x = \dfrac{{36}}{9} = 4 \\
\]
Thus, we get the value of $x = 4$ as the solution for the given equation.

Note: We can add, subtract, multiply or divide both sides of an equation by the same number upholding the equality. We can check whether our solution is correct or not by putting the result in the original given equation \[4x - 24 = - 5x + 12\]. Putting the value of $x = 4$ in the LHS, we get: $4 \times 4 - 24 = 16 - 24 = - 8$, and in the RHS we get: $ - 5 \times 4 + 12 = - 20 + 12 = - 8$. Since, LHS = $ - 8$ = RHS, we can say that our solution is correct.