Equations, inequalities and graphs

Question 1

Solve the equation |2x-5|=|4-x|

Answer 1

2x-5=4-x
3x=9
x=3
or
2x-5=-(4-x)
x=1
OR
(2x-5)²=(4-x)²
4x²-20x+25=x²-8x+16
3x²-12x+9=0
x²-4x=0
(x-3)(x-1)=0
x=3 or x=1

Question 2

How to solve equations of the form |ax+b|=c and |ax+b|=cx+d and |ax²+bx+c|=d?

Answer 2

Solve ax+b=c and ax+b=-c

Question 3

|a|<=b

Answer 3

-b<=a<=b

Question 4

|a|>=b

Answer 4

a<=-b or a>=b

Question 5

|a|>|b|

Answer 5

a²>b²

Question 6

|a|<|b|

Answer 6

a²<b²