Question

How do you solve \[0.5\left( 2x+8 \right)=x-4\]?

Answer 1

Hint:Remove the bracket by multiplying the constant 0.5 with each term inside the bracket. Now, rearrange the terms by taking the terms containing the variable x to the L.H.S. while taking all the constant terms to the R.H.S. Use simple arithmetic operations like addition or subtraction to simplify both the sides and solve for the value of x.

Complete step by step answer:
Here, we have been provided with the linear equation \[0.5\left( 2x+8 \right)=x-4\] and we are asked to solve this equation, that means we have to find the values of x.
Now, removing the bracket by multiplying the constant 0.5 with each term inside the bracket, we get,
\[\Rightarrow x+4=x-4\]
As we can see that the given equation is a linear equation in one variable which is x, so taking the terms containing the variable x to the L.H.S. and taking all the constant terms to the R.H.S., we get,
\[\begin{align}
& \Rightarrow x-x=-4-4 \\
& \Rightarrow x-x=-8 \\
\end{align}\]
On simplifying the L.H.S. we get,
$0 = -8$
Now, in the above relation we get 0 equal to -8 which is not possible. Therefore, the above given linear equation has 0 solutions.

Note: One may note that if the given equation would have been \[0.5\left( 2x+8 \right)=x-4\] then we would have obtained infinite solutions as both the sides would have contained the same expression in x. Note that for the equation to have a unique solution we need the coefficient of x different on both the sides. Never try to solve the above equation using the hit – and – trial method because you will not get any value of x for which L.H.S. = R.H.S.