Question

Solve the equation, given that -1/3 is a root.

a) 3x + 1 = 0
b) 3x - 1 = 0
c) x + 3 = 0
d) x - 3 = 0

Answer 1

The equation that has -1/3 as a root is 3x + 1 = 0. By substituting x = -1/3 into the equation, it simplifies to 0, confirming that -1/3 is indeed a root of the equation.

Step-by-step explanation:

To solve the equation given that -1/3 is a root, we need to find which equation has -1/3 as a solution. To do this, we can substitute x = -1/3 into each of the given equations and see which one holds true:

• 3x + 1 = 0: If x = -1/3, then 3(-1/3) + 1 = 0, which simplifies to -1 + 1 = 0. So, this equation is correct because it equals zero when x is -1/3.
• 3x - 1 = 0: If x = -1/3, then 3(-1/3) - 1 = -2, which is not equal to zero. This equation is incorrect.
• x + 3 = 0: If x = -1/3, then -1/3 + 3 does not equal zero. This equation is incorrect.
• x - 3 = 0: If x = -1/3, then -1/3 - 3 does not equal zero. This equation is incorrect.

Therefore, the equation that has -1/3 as a root is a) 3x + 1 = 0.