Question

Consider the equation 3x−7=2. It has __________ valid solution(s) and __________ extraneous solution(s).

a) One; no
b) No; one
c) Two; no
d) No; two

Answer 1

The equation 3x-7=2 has one valid solution and no extraneous solutions. By isolating the variable x and solving for it, we find that x=3 is the valid solution to the equation.

Step-by-step explanation:

The equation 3x - 7 = 2 has one valid solution and no extraneous solution.

To find the solution, we can isolate the variable x by adding 7 to both sides of the equation. This gives us 3x = 9. Then, we divide both sides of the equation by 3 to solve for x, yielding x = 3.

Substituting this value back into the original equation, we have 3(3) - 7 = 2. Simplifying, we get 9 - 7 = 2, which is true. Therefore, x = 3 is a valid solution to the equation.