# How do I solve this: (2x-3)/(x+1) >= 3 ?!?

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!

• 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:

(2x-3)/(x+1) >= 3

(2x-3)/(x+1) – 3 >= 0 =====> Bring 3 to LHS

(2x-3)/(x+1) – (3x+3)/(x+1) >= 0

(-x-6)/(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 (2x-3)/(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

• 2x-3 X 1

• Multiply both sides by denominator and you will get

(2x-3)=3*(x+1)

Distribute

2x-3=3x+3

Separate the variables and constants

-3-3=3x-2x

-6=x

• Two side multiply (x+1)

2x-3>=3(x+1)

2x-3>=3x+3

2x-3x>=3+3

-x>=6

x<= -6

• 2x-3 = 3(x+1)

2x-3 = 3x+3

-6 = x

• -3x+6-1/2x+2>1/4x+3-16 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

• (2x-3)/(x+1) >= 3

2x -3 >= 3( x+1)

2x – 3 >= 3x +3

2x – 3x >= 3 + 3

-x >= 6

x <= 6 except x = -1