Is the following always, sometimes, or never true?
14 + 3x – 7 = 7x + 7 – 4x
Responses:
a) always
b) sometimes
c) never
b) sometimes
To determine whether the equation 14 + 3x - 7 = 7x + 7 - 4x is always, sometimes, or never true, we can start by simplifying both sides of the equation.
On the left side, we have:
14 + 3x - 7 = 7x + 7 - 4x.
Simplifying the left side:
14 + 3x - 7 = 7x + 7 - 4x
(14 - 7) + 3x = (7x - 4x) + 7
7 + 3x = 3x + 7.
Now, let's simplify the right side:
7x + 7 - 4x = 3x + 7.
So, the equation simplifies to:
7 + 3x = 3x + 7.
At this point, it is clear that we have the same expression on both sides of the equation. Therefore, the equation is always true, regardless of the value of x.
Therefore, the answer is: a) always true.