Question

LaShawn solved the equation below to the determine the solution.3x-8= - x + 4(x-2)How many solutions does LaShawn’s equation have?
a.zerob)onec)twod) Infinitely many

Answer 1

Hi there!

Let's solve this equation step by step!
$3x - 8 = - x + 4(x - 2)$

First work out the parenthesis on the left side. This can for instance be done using rainbow technique.
$3x - 8 = - x + 4x - 8$

Collect the terms on the left
(add 4x to -x).
$3x - 8 = 3x - 8$

Now we can see that we have two identical expressions. Therefore, it doesn't matter what value of x you plug into the equation, the equation will always be true. Hence, the answer is D. [the equation has] infinitely many [solutions].

~ Hope this helps you!

Answer 2

Let's expand both sides of the equation:

Simplify the right hand side:

This is an identity, i.e. the expression in both sides are identical. This means that, whatever value for x you choose, the expression will be true.

So, there are infinitely many solutions, since every possibile value for x is a solution for this equation