I need help on this question

Correct The recommended answer under D. is correct

Step-by-step explanation:

Let us first define the absolute value:

| 7x + 12 |  = 1. { 7x+12 with condition 7x+12≥ 0 or x ≥ - 12/7}

              or 2. { - (7x+12) with condition x < - 12/7}

1.  7x + 12 = 12 ⇒ 7x = 12 - 12 = 0  ⇒ 7x = 0 ⇒ x₁ = 0 ∧ x ≥ - 12/7

the solution is accepted because it is within the interval required by the condition,  so x₁ = 0

2. - (7x + 12) = 12 ⇒ - 7x - 12 = 12 ⇒ - 7x = 24

when we multiply both sides of the equation by -1 we get:

7x = - 24 ⇒ x₂ = - 24/ 7 ∧ x < - 12/7

the solution is accepted because it is within the interval required by the condition, so x₂ = - 24/7

Therefore we have two solutions of a given equation:

x₁ = 0 and x₂ = - 24/7  or  

x ∈ { 0 , - 24/7 }

God is with you!!!

the first one, all those points on the line just make a strait line.