Question

How do you simplify 4x – 3(2 – x)?

Answer 1

We will first use the distributive property in 3(2 – x) and then we will just combine the like terms (club the constants and the like terms) to get the required answer.

Complete step by step solution:
We are given that we are required to simplify 4x – 3(2 – x).
Now, we know that we can use distributive property in the part 3 (2 – x) of the given expression.
Using distributive property in 3 (2 – x), we will then obtain the following equation with us:-
$\Rightarrow$3 (2 – x) = 3(2) – 3x
Simplifying the right hand side of the above equation, we will then obtain the following equation with us:-
$\Rightarrow$3 (2 – x) = 6 – 3x
Now, putting this in the given expression 4x – 3(2 – x), we will then obtain the following equation with us:-
$\Rightarrow$4x - 3 (2 – x) = 4x – {6 – 3x}
Simplifying the right hand side of the above equation by removing the parentheses from the expression, we will then obtain the following expression with us:-
$\Rightarrow$4x - 3 (2 – x) = 4x – 6 + 3x
We can also write the above equation as written in the following line:-
$\Rightarrow$4x - 3 (2 – x) = (4 + 3) x – 6
Simplifying the right hand side of the above equation further, we will then obtain the following equation with us:-

$\Rightarrow$4x - 3 (2 – x) = 7x – 6
Thus, we have the required answer.

Note:-
The students must also note that the distributive property, that we mentioned in the above solution basically refers to the following expression:-
If we have three real numbers a, b and c, then the following expression is always true:-
$\Rightarrow$a (b + c) = a.b + a.c
The students must also note that fact that we have used in the above solution:-
For any real numbers a and b, we have: - (a + b) = - a - b