Question

Polynomial Inequality.. got stuck :/

Answer 1

question please

Answer 2

I got up to \[\frac{ x+4 }{ 2x-1} + \frac{ -3(2x-1) }{2x-1}=0\]

Answer 3

The original is x+4 / 2x-1 < 3

Answer 4

\[\frac{ x+4 }{ 2x-1 } < 3\]

Answer 5

x+4<6x-3

Answer 6

5x > 7
x > 7/5

Answer 7

7/5 is part of the answer, but I have no idea what u did lol

Answer 8

one sec

Answer 9

to eliminate denominator, multiplied both side by (2x-1)

Answer 10

\(\bf \cfrac{ x+4 }{ {\color{brown}{ 2x-1}} } < 3\impliedby cross-multiply
\\ \quad \\
x+4<3\cdot {\color{brown}{ (2x-1)}}\implies x+4<6x-3
\\ \quad \\
4+3<6x-x\implies 7<5x\implies \cfrac{7}{5}<x\)

Answer 11

And then just took x and constants in opposite sides of the inequality sign

Answer 12

Yeah I got that far, then got the first thing I put. I was gonna ask if I can cross the (2x-1) out

Answer 13

@jdoe0001 Oh okay! let me study this

Answer 14

\(\bf \cfrac{ x+4 }{ {\color{brown}{ 2x-1}} } < 3\impliedby cross-multiply
\\ \quad \\
x+4<3\cdot {\color{brown}{ (2x-1)}}\implies x+4<6x-3
\\ \quad \\
x+4+3<6x\cancel{-3+3}\implies x+7<6x\implies \cancel{x-x}+7<6x-x
\\ \quad \\
7<5x\implies \cfrac{7}{5}<x\)

slower version

notice, we "add" 3 and then "subtract" x

Answer 15

@jdoe0001 I dont get what you did in the 3rd line... is that where you added 3? From where and why?

Answer 16

I see where, but why? @jdoe0001

Answer 17

You were ok up to this point?\[\large\rm x+4<6x-3\]

Answer 18

No I got up to x+7 < 6x then I didnt understand

Answer 19

:(