Solve each of the following in equations and represent the solution se

1.	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
Answer» 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 \(\frac{3}{2}< x < \frac{7}{3}\)

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

Answer»

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

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