Solve each absolute value equation for x Solve each absolute

Solve each absolute value equation for x.

Solve each absolute value inequality: express the solution set in interval notation, and graph it.

Please solve, show your work and graph. Thank you.

|5x +2/3| = |x -1/4|

(5x+2/3) and (x-1/4)>0

5x +2/3 = x-1/4

4x = -1/4 -2/3

= (-3-8)/12

x = -11/48

for (5x+2/3) > and (x-1/4)<0

5x +2/3 = - (x- 1/4)

5x +2/3 = -x +1/4

6x = 1/4 -2/3

6x = (3 -8)/12

x = -5/72

Solution : x= -11/12 , -5/72

2) |x-2 |>=4

x-2 >0 \' x-2 >=4

x>= 6

x-2<0 ; -(x-2) >=4

-x +2 >=4

x<= -2

Solution : (-inf, -2] U [ 6 , inf)

|x +2| <=4

for x+2>0;

x+2 <=4

x<=2

x+2<0 ; -x -2 <=4

x>=-6

Solution : [-6 , 2]