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in Linear Equations by (15.7k points)

Solve each of the following in equations and represent the solution set on the number line.

\(\frac{2{\text{x}}-3}{3{\text{x}}-7}\)< 0, x ∈ R

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1 Answer

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by (15.2k points)

Given:

 \(\frac{2{\text{x}}-3}{3{\text{x}}-7}\)< 0, x ∈ R

Signs of 2x – 3:

2x – 3 = 0 → x = \(\frac{3}{2}\)

(Adding 3 on both the sides and then dividing both sides by 2)

2x – 3 < 0 → x > \(\frac{3}{2}\)

(Adding 3 on both the sides and then dividing both sides by 2)

Signs of 3x – 7:

3x – 7 = 0 → x = \(\frac{7}{3}\)

(Adding 7 on both the sides and then dividing both sides by 3)

3x – 7 < 0 → \(x< \frac{7}{3}\)

(Adding 7 on both the sides and then dividing both sides by 3)

3x – 7 > 0 → \(x> \frac{7}{3}\)

(Adding 7 on both the sides and then dividing both sides by 3) 

Zeroes of denominator: 

3x – 7 = 0

x = \(\frac{7}{3}\)

(Adding 7 on both the sides and then dividing both sides by 3) 

Interval that satisfies the required condition: < 0

\(\frac{3}{2}< x < \frac{7}{3}\)

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