Question

Which of the following equations would have no solution?

1) 135x ≥ 143x
2) 135-2x = 143
3) 10x³ = 3
4) -8+16x = 16x-8
5) 4(2x-3) = 8x-12
6) 3(-2x+4) = -6x-12

Answer 1

The equation with no solution is the first one, 135x ≥ 143x, because it implies an impossibility unless a specific condition for x is given, which it is not.

Step-by-step explanation:

To determine which of the given equations would have no solution, we analyze each one individually to see if there's a contradiction or an identity that would indicate the absence or infinity of solutions.

1. 135x ≥ 143x: This equation suggests that a smaller multiple of x is greater than or equal to a larger multiple of x, which is impossible unless x is 0. However, since we are not given such a constraint, this equation would have no solution.
2. 135-2x = 143: This is a solvable linear equation, where x can be found by isolating the variable.
3. 10x³ = 3: This is a cubic equation with one real solution for x.
4. -8+16x = 16x-8: This equation simplifies to 0 = 0, which is an identity, meaning it has an infinite number of solutions.
5. 4(2x-3) = 8x-12: This equation is also an identity after simplification, meaning it has infinite solutions as well.
6. 3(-2x+4) = -6x-12: Simplifying this equation will show that it is an identity too, having infinite solutions.

Therefore, the equation that has no solution is 135x ≥ 143x (option 1).