Is the solution to this rational expression extraneous?
The problem: (2x-3)/7 -(7x)/14
My answer: x = -9/4
My teacher wants to know if the solution is extraneous and I know I have to plug my answer back into the expression to check but I still don't understand.
an expression has no solution.
An equation has a solution.
Plugging in x = -9/4 results in a value of 3/56.
Not sure whether that's what you want. Leaving in x as-is, the expression evaluates to
(-3x-6)/14
Determine Activity of Ca and Cl ions in a solution containing 500 g of a solution of 0.925 g of calcium chloride
To determine if a solution is extraneous, you need to check if it makes the original expression undefined. In this case, the original expression is:
(2x - 3)/7 - (7x)/14
To check if x = -9/4 is extraneous, plug it back into the original expression and simplify:
(2(-9/4) - 3)/7 - (7(-9/4))/14
(-18/4 - 3)/7 - (-63/4)/14
(-18/4 - 12/4)/7 - (-63/4)/14
(-30/4)/7 - (-63/4)/14
(-15/2)/7 - (-9/2)
(-15/2) * (1/7) + (9/2)
-15/14 + 9/2
-15/14 + 63/14
(63 - 15)/14
48/14
24/7
Since plugging x = -9/4 back into the expression yields a defined value (24/7), the solution x = -9/4 is not extraneous. It is a valid solution to the rational expression.