Question

How do you solve $4( - 3x + 1) = - 10(x - 4) - 14x$?

Answer 1

Hint: In this question, we have been given an equation and we are asked to solve it. We need to put all terms in the proper manner then simplify the obtained equation. Then we will simplify the equation and we will get the value of variable $x.$

Complete step-by-step solution:
Given $4( - 3x + 1) = - 10(x - 4) - 14x$
To find: The value for $x$
We need to open the brackets first.
$ \Rightarrow 4 \times ( - 3x) + 4 \times 1 = - 10 \times x - ( - 10) \times 4 - 14x$
Now, we will multiply the required terms. We will get –
$ \Rightarrow - 12x + 4 = - 10x + 40 - 14x$
Now, we will just added the like terms where needed,
We can have,
$ \Rightarrow - 12x + 4 = - 24x + 40$
Now, we will separate the variable terms on the same side and integers on the same side
Hence, we get
$ \Rightarrow - 12x + 24x = 40 - 4$
Now, we just subtract the left side terms because we know the combination of signs
$( - )( + ) = ( - )$
And in the right side we just subtract the integers
Thus, we get,
$ \Rightarrow 12x = 36$
Now we need to find the value for the variable $x$ by dividing
$ \Rightarrow x = \dfrac{{36}}{{12}}$
We get the value for the required $x$ is achieved.
$ \Rightarrow x = 3$

Hence, the required value of $x$ is 3.

Note: We can check the answer by substituting the obtained value in the above equation. If the equation is satisfied, the value is correct.
Our equation is –
$4( - 3x + 1) = - 10(x - 4) - 14x$
So, we need to substitute the value of $x$here
$4( - 3x + 1) = - 10(x - 4) - 14x$
$4( - 3(3) + 1) = - 10((3) - 4) - 14(3)$
We just multiply where the requirement and on simplifying the equation,
We can have
$4( - 9 + 1) = - 10( - 1) - 42$
We just use the sign combination $( - )( - ) = ( + )$in the right side of the above expression, we get
$4( - 8) = 10 - 42$
By multiplying the terms in the left-hand side and the subtract the two terms in the right-handed side Hence we get,
$ - 32 = - 32$
$\therefore $L.H.S = R.H.S
So, we get the left-hand side equal to the right-hand side.
Therefore, we can verify our answer by substituting the value in the expression or in the given equation.