Answer:
Correct answer: 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 }
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