Solving inequalities for 'x'

How would you solve |2x-5| + 3 < 10

I2x-5I+3<10 subtract 3 from each side
I 2x-5 I < 7

let us inspect y = I X I this is a V shaped curve with vertex at x=0
We can rewrite the curves as
y=x for x greater than 0
y=-x for x less than 0

let us inspect I 2x-5 I
This is a V shaped curve with vertex at x=5/2.
we can replace I2x-5L with two equations one for x>5/2 and for one x less than 5/2

2x-5<10 for x>5/2
2x<15 for x<5/2
x<7.5 for x>5/2
for 2.5<x<7.5 I 2x-5 I<7 is true answer

-[2x-5]<10 for x<5/2
-2x+5<10 add 2x to each side
5<2x +10 subtract 10 from each side
2x>-5
x>-2.5

for -2.5< x < 2.5 I 2x-5 I <10 answer

-2.5 <x < 7.5 answer
2x<-5 for x<5/2
x<-5/2 for x<5/2
for