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.

Respuesta :

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
The correct answer is A)

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

(1) [tex]\left | 3x-1 \right |+7=2[/tex]

∴ [tex]\left | 3x-1 \right |=-5[/tex]

(2) [tex]\left | 2x+1 \right |+4=3[/tex]

∴ [tex]\left | 2x+1 \right |=-1[/tex]

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

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