The number of elements in the set x ∈ R :(|x|-3)|x+4|=6 is equal to

Question

The number of elements in the set x ∈ R :(|x|-3)|x+4|=6 is equal to (A) 3 (B) 2 (C) 4 (D) 1

Tardigrade Admin · Accepted Answer

x ≠- 4 (|x|-3)(|x+4|)=6 ⇒ |x|-3=(6/|x+4|) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/1b08a4261fdce9618eaae2c93c398e56-.png" /> No. of solutions = 2

Q. The number of elements in the set ${x \in R : (∣ x ∣ - 3) ∣ x + 4∣ = 6}$ is equal to

3

2

4

1

$x \neq = - 4$
$(∣ x ∣ - 3) (∣ x + 4∣) = 6$
$\Rightarrow ∣ x ∣ - 3 = \frac{6}{∣ x + 4∣}$

No. of solutions $= 2$

Q. The number of elements in the set {x∈R:(∣x∣−3)∣x+4∣=6} is equal to

3

2

4

1

x=−4 (∣x∣−3)(∣x+4∣)=6 ⇒∣x∣−3=∣x+4∣6​ No. of solutions =2

Q. The number of elements in the set ${x \in R : (∣ x ∣ - 3) ∣ x + 4∣ = 6}$ is equal to

$x \neq = - 4$
$(∣ x ∣ - 3) (∣ x + 4∣) = 6$
$\Rightarrow ∣ x ∣ - 3 = \frac{6}{∣ x + 4∣}$

No. of solutions $= 2$