Question

The table below shows two equations:
Equation 1 |3x − 1| + 7 = 2
Equation 2 |2x + 1| + 4 = 3

Which statement is true about the solution to the two equations? (1 point)

A) Equation 1 and equation 2 have no solutions.
B) Equation 1 has no solution, and equation 2 has solutions x = 0, 1.
C) The solutions to equation 1 are x = −1.3, 2, and equation 2 has no solution.
D) The solutions to equation 1 are x = −1.3, 2, and equation 2 has solutions x = 0, 1.

Answer 1

The correct answer is option A A) Equation 1 and equation 2 have no solutions For the equation 1 l 3x-1 l +7=2 l 3x-1 l = 2-7 =-5 The absolute value should be positive So, there is no solution For the equation 2 l 2x+1 l +4 = 3 l 2x+1 l = 3 - 4= -1 The absolute value should be positive So, there is no solution

Answer 2

The correct answer is A)

The proof for the veracity is that we have these two equations:

(1) $\left | 3x-1 \right |+7=2$

∴ $\left | 3x-1 \right |=-5$

(2) $\left | 2x+1 \right |+4=3$

∴ $\left | 2x+1 \right |=-1$

Given that because of the property of Absolute Value Function $\left | 3x-1 \right |\geq0$ and $\left | 2x+1 \right | \geq 0$ (it must be so) then there is not possible for the equation (1) and (2) to be true.