Question

Solve the following equation 2x+4/x-1 >5 ​

Answer 1

We have
x−1
2x+4
​
≥5⇒
x−1
2x+4
​
−5≥0
⇒
x−1
2x+4−5(x−1)
​
≥0⇒
x−1
2x+4−5x+5
​
≥0
x−1
−3x+9
​
≥0 [Multiplying both sides by -1]
x−1
3x−9
​
≤0⇒
x−1
3(x−3)
​
≤0 [Dividing both sides by 3]
x−1
x−3
​
≤0⇒1Hence the solution set of the given inequations is (1, 3]

Answer 2

Answer:

Answer

We have

x−1

2x+4

≥5⇒

x−1

2x+4

−5≥0

⇒

x−1

2x+4−5(x−1)

≥0⇒

x−1

2x+4−5x+5

≥0

x−1

−3x+9

≥0 [Multiplying both sides by -1]

x−1

3x−9

≤0⇒

x−1

3(x−3)

≤0 [Dividing both sides by 3]

x−1

x−3

≤0⇒1<x≤3⇒x∈(1,3]

Hence the solution set of the given inequations is (1, 3]