Question

How do you simplify $3\left( {2x - 4} \right) - 2\left( {5x - 1} \right)$?

Answer 1

Hint: In this problem we have given the subtraction of two terms and each term is multiplied by one integer and there is one unknown in the given term. And we asked to simplify the given term. We can find the result of the given term by multiplying, expanding, grouping and using distributive property.

Formula used:
$a\left( {x - y} \right) = ax - ay$

Complete step by step answer:
Given term is $3\left( {2x - 4} \right) - 2\left( {5x - 1} \right)$
Here we asked to simplify the given term. So to simplify the given term we are going to use the distributive property.
First, we have to apply the distributive property to the terms $3\left( {2x - 4} \right)$and$2\left( {5x - 1} \right)$then use subtraction to get the result.
$ \Rightarrow 3\left( {2x - 4} \right) - 2\left( {5x - 1} \right) = 3 \times 2x - 3 \times 4 - 2 \times 5x + 2 \times 1$,
On simplifying we get
$ \Rightarrow 3\left( {2x - 4} \right) - 2\left( {5x - 1} \right) = 6x - 12 - 10x + 2$,
Let us adding the coefficients $x$ and adding numbers, we get
$ \Rightarrow 3\left( {2x - 4} \right) - 2\left( {5x - 1} \right) = - 10 - 4x$,

Hence, the given term is simplified- 10 - 4x

Additional information:
According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the product together. The distributive property tells us how to solve expressions in the form of $x\left( {a + b} \right)$. The distributive property is sometimes called the distributive law of multiplication and division.

Note: There is an unknown variable in the given term which is $x$. And we have the same unknown variable in the result also. That is we just simplified or expanded the given term using the distributive property. If the given term is equal to zero then we could find the value of the unknown variable $x$. We have remembered to multiply first, before going to the addition.