Question

How do you solve $4x = - 16?$

Answer 1

Hint: In the question we are given an equation in terms of x and we need to solve this equation. i.e. we need to find the value of the variable x. In order to find the value of x, we make use of some basic mathematical expressions. In the above problem first divide the both sides of the equation by 4 and then solve for x.
Also we can verify our obtained value of x by substituting back in the given equation.

Complete step by step solution:
Here given an equation $4x = - 16$ ……(1)
First we will try to understand the meaning of the given equation.
Here $4x$ simply means 4 is multiplied to an unknown variable x whose values we have to determine.
Now we divide both sides of the equation by 4 and simplify to obtain the value of x.
Dividing by 4 on both sides of the equation (1), we get,
$\dfrac{{4x}}{4} = \dfrac{{ - 16}}{4}$ ……(2)
Now we simplify both the sides.
Solving L.H.S. we get, $\dfrac{{4x}}{4} = x$.
Solving R.H.S. we get, $\dfrac{{ - 16}}{4} = - 4$
Now substituting in the equation (2) we get,
$\dfrac{{4x}}{4} = \dfrac{{ - 16}}{4}$
$ \Rightarrow x = - 4$.
Hence the solution of $4x = - 16$ is $x = - 4$.
We can check whether the value of x is correct or not by substituting it back in the given equation.
If we get L.H.S. is equal to R.H.S. then the x value satisfies the equation.
Substituting $x = - 4$ in the equation (1), we get,
$4x = - 16$
$ \Rightarrow $$4( - 4) = - 16$
$ \Rightarrow - 16 = - 16$
Hence L.H.S. is equal to R.H.S.

Therefore the required value of x is, $x = - 4$.

Note:
Alternative method :
Given an equation $4x = - 16$.
Transfer the coefficient -16 to the L.H.S. and then solve the equation.
Remember that when we transfer any variable or number to the other side, the signs of the same will be changed to the opposite sign.
Taking -16 to the L.H.S. we get,
$ \Rightarrow $$4x + 16 = 0$
Taking 4 as common on L.H.S. we get,
$ \Rightarrow 4(x + 4) = 0$
Dividing both sides of the equation by 4, we get,
$ \Rightarrow \dfrac{{4(x + 4)}}{4} = \dfrac{0}{4}$
$ \Rightarrow x + 4 = 0$
Taking 4 to the R.H.S. we get,
$ \Rightarrow x = - 4$.
Hence, the required value of x is, $x = - 4$.
We need to be careful while taking the terms to the other side. When transferring any variable or number to the other side, the sign of the same will be changed to its opposite sign.
It is important to know the following basic facts.
An equation remains unchanged or undisturbed if its satisfies the following conditions.
(1) If L.H.S. and R.H.S. are interchanged.
(2) If the same number is added on both sides of the equation.
(3) If the same number is subtracted on both sides of the equation.
(4) When both L.H.S. and R.H.S. are multiplied by the same number.
(5) When both L.H.S. and R.H.S. are divided by the same number.