Absolute Eqution Help!!

[TStiles4]

|4x+1| = |x-3|

 

[arthur ohlsten]

To aid in the problem let us first sketch the two curves I 4x+1 I and Ix-3 I

I 4x+1I is a V shaped curve with vertex at -1/4. for values above -1/4 the slope is 4.
for values below x=-1/4 the slope is -4.

I x-3 I is a V shaped curve vertex at x=3 and slope of 1 for x>3 and slope -1 for x<3

STEP 1
let us see if the curve I x-3 I for x>3 ever crosses I 4x+1I for x>-1/4
4x+1= x-3 for x>3
3x=-4
x=-4/3 answer no because this point is not above x=3

step 2
let us see if I x-3I x<3 ever crosses I4x+1I for x> -1/4
-[x-3]=4x+1
-x+3=4x+1
5x=2
x=2/5 yes this is above x=-1/4

step 3
does I x-3 I for x<3 ever cross I 4x+1 I for x<-1/4
-[x-3]=-[4x+1] for x<-1/4
-x+3=-4x-1
3x= -4
x=-3/4 yes this is less than -1/4

x=2/5 and x=-3/4 the absolute equation is true

Please check for errors
Arthur

 

[Mrspi]

|4x+1| = |x-3|

If

| a | = | b|, then

a[sup:27i7ote7]2[/sup:27i7ote7] = b[sup:27i7ote7]2[/sup:27i7ote7]

Since

|4x + 1| = |x - 3|

(4x + 1)[sup:27i7ote7]2[/sup:27i7ote7] = (x - 3)[sup:27i7ote7]2[/sup:27i7ote7]

16x[sup:27i7ote7]2[/sup:27i7ote7] + 8x + 1 = x[sup:27i7ote7]2[/sup:27i7ote7] - 6x + 9

Solve this quadratic equation....