Question

How do you solve $3(6 - x) + 2x = 15$?

Answer 1

Hint: In this question, we are asked to solve the equation by finding the value of the variable x. So, firstly multiply 3 to $(6 - x)$ using the distributive property of subtraction. Then combine the like terms and simplify. After that keep the terms with the variable x to one side and transfer all the constant terms to another side. And then find the value of the variable x.

Complete step by step answer:
Given an equation of the form,
 $3(6 - x) + 2x = 15$ …… (1)
We need to solve the above equation to find the value of the unknown variable x.
To the first to simplify we use the distributive property of subtraction and proceed.
The distributive property of subtraction is given by,
$a(b - c) = a \cdot b - a \cdot c$
Consider the term $3(6 - x)$.
Here $a = 3$, $b = 6$ and $c = x$.
Now using the property we get,
$3(6 - x) = 3 \cdot 6 - 3 \cdot x$
$ \Rightarrow 18 - 3x$
Hence the equation (1) becomes,
$ \Rightarrow 18 - 3x + 2x = 15$
Now combining the like terms $ - 3x + 2x = - x$
Hence we have,
$ \Rightarrow 18 - x = 15$
Now to solve the problem, we have to get the variable x. So, to do this we have to get rid of the constant term 18.
So we subtract 18 from both sides of the equation we get,
$ \Rightarrow 18 - 18 - x = 15 - 18$
$ \Rightarrow 0 - x = - 3$
$ \Rightarrow - x = - 3$
Now we are one step away from the answer. We cannot have the variable x as a negative number here. So we make it positive.
To do this, we multiply both the sides of the equation by $ - 1$, we get,
$ \Rightarrow - 1 \times - x = - 1 \times - 3$
$ \Rightarrow x = 3$

Hence, the solution for the equation $3(6 - x) + 2x = 15$ is $x = 3$.

Note: In such types of equations students mainly forget to apply the correct mathematical operation on the equation such that the expression gets simplified. It is important to make the right choice to solve this type of problem. We can check whether the obtained answer is correct by substituting back in the given equation. If the equation satisfies then our value for the variable is correct.
It is important to know the following basic facts.
An equation remains unchanged or undisturbed if it 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