Question

How do you solve $-31-4x=-5-5(1+5x)$ ?

Answer 1

Hint: Since the equation given to us is a linear equation, we will rearrange the terms and perform various operations such as multiplication and division on either side of the expression to get the value of $x$ which is the final answer and then we will cross check whether the solution we found is correct by resubstituting it in the given expression.

Complete step by step answer:
We have the given equation as $-31-4x=-5-5(1+5x)$, it can be written as:
$\Rightarrow -31-4x=-5-5(1+5x)$
We will first open the brackets on the right-hand side of the equation.
$\Rightarrow -31-4x=-5-5\times 1-5\times 5x$
On simplifying the bracket, we get:
$\Rightarrow -31-4x=-5-5-25x$
On simplifying the terms in the right-hand side, we get:
$\Rightarrow -31-4x=-10-25x$
Now we will take the similar terms on the same side, on transferring $25x$ from the right-hand side to the left-hand side and transferring $-31$ from the left-hand side to the right-hand side, we get:
$\Rightarrow 25x-4x=-10+31$
On simplifying the left-hand side, we get:
 $\Rightarrow 21x=-10+31$
On simplifying the right-hand side, we get:
$\Rightarrow 21x=21$
Now on transferring $21$ from the left-hand side to the right-hand side we get:
 $\Rightarrow x=\dfrac{21}{21}$
On simplifying the fraction, we get:
 $\Rightarrow x=1$, which is the final answer.

Note: Now to check whether the answer is correct, we will substitute the value of $x=1$ in the equation.
On substituting $x=1$ in the left-hand side of the equation, we get:
 $\Rightarrow -31-4(1)$
On simplifying we get:
$\Rightarrow -31-4$
which is $-35$ , therefore the value of the left-hand side is $-35$ .
Now on substituting $x=1$ in the right-hand side of the equation, we get:
$\Rightarrow -5-5(1+5(1))$
On simplifying the brackets, we get:
$\Rightarrow -5-30$
On simplifying the term, we get:
$\Rightarrow -35$
since the value of the left-hand side is equal to the value of the right-hand side, the answer is correct.
It is to be remembered that the equation given above is a linear equation which has only one variable which is $x$ .
when there is one variable in an equation, we can find its solution by addition or subtraction, when there are two or more than two variables in the equation, we need that many equations to solve the question. The solution can be found using elimination method or by using a matrix.