Question

If 3-4x is in modulus,greater than equal to 9 than the value of x is

Answer 1

We have to find the value of x if |3 - 4x| ≥ 9

Solution : |3 - 4x|≥ 9

we know, if |a| ≥ b where b > 0

Then, a ≥ b or, a ≤ -b

so, |3 - 4x| ≥ 9 ⇒(3 - 4x) ≥ 9 or, (3 - 4x) ≤ -9

(3 - 4x) ≥ 9

⇒3 - 9 ≥ 4x

⇒-6 ≥ 4x

⇒x ≤ -3/2

Again, (3 - 4x) ≤ -9

⇒3 + 9 ≤ 4x

⇒12 ≤ 4x

⇒x ≥ 3

Therefore the value of x is (-∞ , -3/2] U [3, ∞)

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Answer 2

Answer:-

We have to find the value of x if |3 - 4x| ≥ 9

Solution :

|3 - 4x|≥ 9

we know,

if |a| ≥ b where b > 0

Then,

a ≥ b or, a ≤ -b

so, |3 - 4x| ≥ 9 ⇒(3 - 4x) ≥ 9 or, (3 - 4x) ≤ -9

(3 - 4x) ≥ 9

⇒3 - 9 ≥ 4x

⇒-6 ≥ 4x

⇒x ≤ -3/2

Again,

(3 - 4x) ≤ -9

⇒3 + 9 ≤ 4x

⇒12 ≤ 4x

⇒x ≥ 3

Therefore the value of x is (-∞ , -3/2] U [3, ∞)

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