Question

How do you solve $8(x - 3) = 96$ using the distributive property?

Answer 1

Hint:First remove parentheses from the expression using distributive property of multiplication, then with the help of algebraic operations simplify the expression such that variables and constants will be on opposite sides, generally variables on L.H.S. (Left hand side) and constants on R.H.S. (Right hand side). And then divide both sides with the coefficient of the variable in order to get the solution.Distributive property of multiplication is given as $a(b + c) = ab + ac$.

Complete step by step answer:
To solve the expression $8(x - 3) = 96$ we need to remove the parentheses from it and simplify further, for removing the parentheses in the expression we can see that it is multiplied with a number, so we will use the distributive property of multiplication in order to remove the parentheses. Distributive property of multiplication can be understood as
$a(b + c) = ab + ac$. Using this for given expression, we will get
$
8(x - 3) = 96 \\
\Rightarrow 8x - 8 \times 3 = 96 \\
\Rightarrow 8x - 24 = 96 \\ $
Now we can see that on the left hand side there is a constant $( - 24)$ we have to remove that constant by adding $24$ both sides, we will get
$
\Rightarrow 8x - 24 = 96 \\
\Rightarrow 8x - 24 + 24 = 96 + 24 \\
\Rightarrow 8x - 0 = 120 \\
\Rightarrow 8x = 120 \\ $
Dividing both the sides with coefficient of $x$ in order to get the required solution
$
\Rightarrow 8x = 120 \\
\Rightarrow \dfrac{{8x}}{8} = \dfrac{{120}}{8} \\
\therefore x = 15 \\ $
Hence, $x = 15$ is the required solution for the expression $8(x - 3) = 96$.

Note:Distributive property is nothing but the distribution of multiplication over addition or subtraction. It says that multiplying two or more addends by a number will be equal to the multiplication of each addend separately with the number and then adding them.Even division is an inverse function of multiplication but this property holds good for it only when the dividend is distributed.