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# Solve for x: |3x-7|<5

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Joined: 23 Feb 2015
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18 Nov 2019, 11:29
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Difficulty:

25% (medium)

Question Stats:

74% (01:04) correct 26% (02:40) wrong based on 31 sessions

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Solve for x: $$|3x-7|<5$$
A) x∈ (2, 12)
B) x∈ (-∞, -2) ∪ (12, ∞)
C) x∈ ($$\frac{2}{3}$$, 4)
D) x∈ (-∞, $$\frac{2}{3}$$) ∪ (4, ∞)
E) x∈ (-∞, -4) ∪ ($$\frac{2}{3}$$, ∞)

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Posts: 8310
Re: Solve for x: |3x-7|<5  [#permalink]

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23 Nov 2019, 20:33
Solve for x: $$|3x-7|<5$$
A) x∈ (2, 12)
B) x∈ (-∞, -2) ∪ (12, ∞)
C) x∈ ($$\frac{2}{3}$$, 4)
D) x∈ (-∞, $$\frac{2}{3}$$) ∪ (4, ∞)
E) x∈ (-∞, -4) ∪ ($$\frac{2}{3}$$, ∞)

Two cases
1) 3x-7>0
3x-7<5.....3x<12......x<4
2) 3x-7<0
-(3x-7)<5.....3x-7>-5......3x>2.....x>2/3

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Re: Solve for x: |3x-7|<5  [#permalink]

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23 Nov 2019, 23:53
Solve for x: $$|3x-7|<5$$
A) x∈ (2, 12)
B) x∈ (-∞, -2) ∪ (12, ∞)
C) x∈ ($$\frac{2}{3}$$, 4)
D) x∈ (-∞, $$\frac{2}{3}$$) ∪ (4, ∞)
E) x∈ (-∞, -4) ∪ ($$\frac{2}{3}$$, ∞)

As modulus is less than 5, range of x will be finite line segment.
therefore option B, D,E are eliminated

If x = 5, then | 15-7| is not less than 5.
Hence C is correct.
Re: Solve for x: |3x-7|<5   [#permalink] 23 Nov 2019, 23:53
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