Question

Solve the following and Write Answer in Interval Notation. 2|4x-5|-4 ≤ 2x-2

Answer 1

start with
\[2|4x-5|\leq 2x+2\] then divide by 2 to get
\[|4x-5|\leq x+1\] and then you have to work in cases

Answer 2

that is, if \(x\geq\frac{5}{4}\) you know \(|4x-5|=4x-5\) so solve
\[4x-5\leq x+1\]
\[3x\leq 6\]
\[x\leq 2\] so the interval \([\frac{5}{4},2]\) is good

Answer 3

now repeat for \(x\leq \frac{5}{4}\) making \(|4x-5|=5-4x\) and solve
\[5-4x\leq x+1\]

Answer 4

what about the 4 in the beginning of the equation?

Answer 5

i added 4 to both sides as a first step

Answer 6

oh okay

Answer 7

that why i wrote \(2|4x-5|\leq 2x+2\)

Answer 8

when you solve the last inequality, you will get a contradiction
check it and see (don't forget \(x<\frac{5}{4}\)

Answer 9

so the "final answer: is just \([\frac{5}{4},2]\)

Answer 10

alright thanks!

Answer 11

I think its
\[\frac{4}{5}<x<2\]

Answer 12

2|4x-5|-4<2x-2
2|4x-5|<2x+2
|4x-5|<x+1
(4x-5)^2<x^2+2x+1
16x^2-40x+25<x^2+2x+1
15x^2-42x+24<0
(x-2)(5x-4)=0
x=2 x=4/5

Then
4/5<x<2