Which equation has exactly ONE solution?
Responses
A 2+6x2
= 3x + 12 + 6 x 2 = 3x + 1
B 8−4x10
= 8 + 2x8 − 4 x 10 = 8 + 2x
C 15x−53
= 5x + 415 x − 5 3 = 5x + 4
D 4x−102
= 2x − 5
The equation that has exactly ONE solution is D: 4x - 10 = 2x - 5.
The equation that has exactly ONE solution is D: 4x - 10 = 2x - 5.
To determine which equation has exactly one solution, we need to check for the number of solutions each equation can have.
A: `2 + 6x^2 = 3x + 12 + 6 x 2 = 3x + 1`
This equation involves a quadratic term (x^2), which means it could have two solutions: one where the quadratic term is positive, and one where it is negative.
B: `8 − 4x^10 = 8 + 2x`
This equation does not involve any quadratic terms or higher exponents. It is a linear equation, which means it can have exactly one solution.
C: `15x − 53 = 5x + 4`
This equation is a linear equation, with one variable raised to the power of 1. It can also have exactly one solution.
D: `4x − 10^2 = 2x − 5`
This equation has a number raised to the power of 2 (10^2), making it a quadratic equation. It could have two solutions.
Based on the analysis above, the equation B: `8 − 4x^10 = 8 + 2x` is the one that has exactly one solution.