Question

How do you solve $\dfrac{1}{2}(4x - 6) = 11$ using the distributive property?

Answer 1

This question is based on the solution of linear equations in one variable. In this question we need to find the value of $x$, from the given equation $\dfrac{1}{2}(4x - 6) = 11$. It is specified in the question to use the distributive property of multiplication to solve this equation. Distributive property of multiplication is given by $A(B + C) = A \cdot B + A \cdot C$, it is very useful while performing bigger
calculations.

Complete step by step solution:
Let us try to solve this question in which we need to find the value of
$x$ from the given linear equation of one variable $\dfrac{1}{2}(4x - 6) = 11$. We have to solve this using distributive property. Distributive property is given by $A(B + C) = A \cdot B + A \cdot C$. We can also solve this without using distributive property, since it is already stated in the question to use distributive property. So, here is the solution to solve the equation $\dfrac{1}{2}(4x - 6) = 11$ using distributive property.
We will first apply distributive property to the L.H.S of equation, to write it as
$\dfrac{1}{2}(4x - 6) = 11 \\\ \dfrac{1}{2} \cdot (4x) + \dfrac{1}{2} \cdot ( - 6) = 11 \\\$
After applying distributive property we simplify above equation to get,
$2x - 3 = 11$ $eq(1)$
Because both $4x$ and $- 6$ are divisible by$2$. Now to get the value of $x$, we add $3$ to both side of the $eq(1)$, we get
$2x - 3 + 3 = 11 + 3$
Since in L.H.S $- 3$ and $3$ cancels each other, we get
$2x = 14$
Now dividing both side by $2$, we get the value of $x$
$\dfrac{{2x}}{2} = \dfrac{{14}}{2} \\\ x = 7 \\\$
Hence we get the value of $x = 7$solving$\dfrac{1}{2}(4x - 6) = 11$.

Note: While solving for the linear equation of one variable, we need to just clear about the signs of each term from L.H.S to R.H.S or R.H.S to L.H.S. We can also check if our solution is correct or not by putting the value of $x$ back in the equation and get R.H.S equal to L.H.S means the solution is correct. Check the correctness of the solution yourself.