Inequalities 7X+1/X-1≤9

Please show mw the steps the answer is
x<1 or x≥ 5

For x > 1, we see that:
(7x + 1)/(x - 1) ≤ 9
==> 7x + 1 ≤ 9(x - 1), since x - 1 > 0 for x > 1
==> 7x + 1 ≤ 9x - 9
==> 2x ≥ 10
==> x ≥ 5.

Then, for x < 1, we see that:
(7x + 1)/(x - 1) ≤ 9
==> 7x + 1 ≥ 9(x - 1), since x - 1 < 0 for x < 1
==> 7x + 1 ≥ 9x - 9
==> 2x ≤ 10
==> x ≤ 5.

However, since we want x < 1, the solution for this part is x < 1.

Therefore, the answer is x < 1 or x ≥ 5 as required.

I hope this helps!

(7X+1) / (X-1) ≤ 9 ?

Multiply both sides by (x-1),

7x+1 ≤ 9(x-1) ====> 7x+1 ≤ 9x -9

Add (-7x+9) both sides, 1+9 ≤ 2x,

Divide both sides by 2, 5 ≤ x,

Hence, x ≥ 5 >=================< ANSWER

Next time, use parentheses!

(7*x + 1)
------------ ≤ 9
(x - 1)

(7*x + 1)
------------ - 9 ≤ 0
(x - 1)

((7*x + 1) - 9*x + 9) ≤ 0
----------------------------
(x - 1)

(10 - 2*x)
-------------- ≤ 0
(x - 1)

2*(5 - x)
------------ ≤ 0
(x - 1)

(5 - x)
--------- ≤ 0
(x - 1)



5 - x ≤ 0

x ≥ 5

x - 1 ≤ 0

x ≤ 1

Solution:

5 ≤ x ≤ 1