Question

How do you solve $4(5 - x) = 8$ using the distributive property ?

Answer 1

Hint: Here we need to simplify the given algebraic expression using the distributive property. Here we make use of distributive property of subtraction on the L.H.S. of the equation. According to this property, if we have given a, b, c as real numbers, then $a.(b - c) = a.b - b.c$.
So applying this property firstly we multiply the outside number with the inside number. Then we find the difference of these products by subtracting each product. Then we bring the term in the R.H.S. to L.H.S. and simplify it to obtain the value of the variable x.

Complete step by step solution:
Given the equation $4(5 - x) = 8$. …………….. (1)
It is mentioned that we need to make use of distributive property.
Here we make use of distributive property of subtraction to the L.H.S. of the equation.
According to this property, the difference of two numbers multiplied by the third number is equal to the difference of each number multiplied by the third number.
For instance, consider the equation $a.(b - c)$
Where a, b, c are any real numbers.
When we apply distributive property we have to multiply a with both b and c and then take the difference of them.
i.e. $a.(b - c) = a.b - b.c$ ……(2)
Consider the L.H.S. of the equation (1) given by $4(5 - x)$.
Here we note that $a = 4$, $b = 5$ and $c = x$.
Now applying distributive property given in the equation (2), we get,
$4(5 - x) = 4.5 - 4.x$
$ \Rightarrow 4(5 - x) = 20 - 4x$
Now substituting back in the equation (1) and solving it to obtain the value of the variable x.
Put $4(5 - x) = 20 - 4x$in the equation (1), we get,
$20 - 4x = 8$
Now subtract 8 from both the sides we get,
$ \Rightarrow 20 - 4x - 8 = 8 - 8$
Reorder the terms in the L.H.S. we get,
$ \Rightarrow $$20 - 8 - 4x = 8 - 8$
Now computing like terms on L.H.S. $20 - 8 = 12$
$ \Rightarrow 12 - 4x = 0$
Now add $4x$ on both sides, we get
$ \Rightarrow 12 - 4x + 4x = 4x$
Computing like terms on L.H.S. $ - 4x + 4x = 0$
$ \Rightarrow 12 + 0 = 4x$
$ \Rightarrow 12 = 4x$
Now dividing by 4 on both sides, we get,
$ \Rightarrow \dfrac{{12}}{4} = \dfrac{{4x}}{4}$
$ \Rightarrow 3 = x$
Hence we get $x = 3$.

Therefore the solution for $4(5 - x) = 8$ using distributive property is $x = 3$.

Note:
The algebraic expression used in the question is a linear algebraic expression because the degree of the expression is 1.
The distributive property applies to the multiplication of a number with the sum or difference of two numbers, i.e. this property holds true for multiplication over addition and subtraction. It simply states that multiplication is distributed over addition or subtraction.
Let a, b, c be any real numbers.
The distributive property of addition is given by,
$a.(b + c) = a.b + b.c$
The distributive property of subtraction is given by,
$a.(b - c) = a.b - b.c$
Also we must know which mathematical expressions have to be used to simplify the equation.