Please explain step by step!!!
the values of x where the absolute values change sign create the difficulty, these points are at x = 0 and x = 3
so you have to test over the three intervals
a) x<0
b) 0≤x<3
c) x≥3
individually
a)
if x < 0 then -2x ≤ -(x-3) which implies x ≥ -3
so you have -3 ≤ x < 0
b)
if 0≤x<3 then 2x ≤ -(x-3) which implies x ≤ 1
so you have 0 ≤ x ≤ 1
c)
if x ≥ 3 then 2x ≤ (x-3) which implies x ≤ -3
so you get a contradiction
combining the intervals from part a) & b) gives
-3 ≤ x ≤ 1
as the solution
.,.,.,.,.,.,.,.
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Verified answer
the values of x where the absolute values change sign create the difficulty, these points are at x = 0 and x = 3
so you have to test over the three intervals
a) x<0
b) 0≤x<3
c) x≥3
individually
a)
if x < 0 then -2x ≤ -(x-3) which implies x ≥ -3
so you have -3 ≤ x < 0
b)
if 0≤x<3 then 2x ≤ -(x-3) which implies x ≤ 1
so you have 0 ≤ x ≤ 1
c)
if x ≥ 3 then 2x ≤ (x-3) which implies x ≤ -3
so you get a contradiction
combining the intervals from part a) & b) gives
-3 ≤ x ≤ 1
as the solution
.,.,.,.,.,.,.,.