Hey guys can you help me solve the above please? I’m really lost.
Thank you luckyboy!!!
I was scrolling down and knew I couldn’t multiply both sides by the denominator so I was a bit worried when I knew everyone was wrong. But then I got to your answer, so thank you mate. I’m leaving this open until the morning to remind myself to check it before hand but if I understand your answer fully in the morning I’ll pick you. Cheers!
12 Answers

I’m sorry to say that all people above are wrong.
True answer: 6 <= x < 1, don’t believe? Try it by your calculator!
Big Mistake:
You can’t multiply (x+1) to both side because you don’t know (x+1) is positive or negative which may infected “>” or “<“.
Working:
(2x3)/(x+1) >= 3
(2x3)/(x+1) – 3 >= 0 =====> Bring 3 to LHS
(2x3)/(x+1) – (3x+3)/(x+1) >= 0
(x6)/(x+1) >= 0
(x+6)/(x+1) <= 0 =========> Multiply both side by 1, change the sign
It shows that (x+6)/(x+1) must be negative value.
(x+6) is positive when x > 6
(x+6) is negative when x < 6
(x+1) is positive when x > 1
(x+1) is negative when x < 1
Two ways for (x+6)/(x+1) to be ve:
(1)(x+6) is negative, x < 6
and (x+1) is positive, x > 1
That is impossible for both case to happen, so rejected.
(2) (x+6) is positive, x > 6
and (x+1) is negative, x < 1
=======> So, answer is 6 < x < 1
But becareful of the question, question says (2x3)/(x+1) >= 3, there is eaual sign, so the answer should have equal sign.
Again, careful, (x+1) is denominator, so x cannot = 3
Final answer: 6 <= x < 1

2x3 X 1

Multiply both sides by denominator and you will get
(2x3)=3*(x+1)
Distribute
2x3=3x+3
Separate the variables and constants
33=3x2x
6=x

Two side multiply (x+1)
2x3>=3(x+1)
2x3>=3x+3
2x3x>=3+3
x>=6
x<= 6

2x3 = 3(x+1)
2x3 = 3x+3
6 = x

3x+61/2x+2>1/4x+316 21>3 1/3x== I GIVE UP!!!!!!

2x – 3 ≥ 3x + 3
– 6 ≥ x
x ≤ – 6

Distribute: 3x – 3 – 8x 12 > 0 Combine like terms 5x – 15 > 0 Add 15 to both sides 5x > 15 Divide both sides by 5 {don’t forget that you have to flip the inequality sign around whenever you multiply or divide both sides of an inequality by a negative number} x < 3

(2x3)/(x+1) >= 3
2x 3 >= 3( x+1)
2x – 3 >= 3x +3
2x – 3x >= 3 + 3
x >= 6
x <= 6 except x = 1

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RE:
How do I solve this: (2x3)/(x+1) >= 3 ?!?
Hey guys can you help me solve the above please? I’m really lost.