Find the solution of the equation 3x 1 5 11 Perform the o

Find the solution of the equation 3|x + 1| - 5 = -11. Perform the operation 1 + i + and write the result in standard form. Solve the inequality x3 - z

Solution

1. slope = 1/2 ; ( 2, -2)

slope intercept form: y = mx +c

y = x/2 +c ----> find c : -2 = 2/2 +c

c = -3 ;

y = x/2 -3

2. |3x +1 | -5 = -11

| 3x +1 | = -6

for 3x +5 > 0 ; 3x +1 =-6

3x = -7 ---> x =-7/3

for 3x +5<0 ; -3x -5 = -6 ---> -3x = -1

x = 1/3

Solution : x= -7/3 , 1/3

3. 1 + i + (5 +i)/2

Taking 2 as LCD : (2 +2*i + 5 +i)/2 = ( 7 +3i)/2

Opition 1

4. x^-2 -2x^-1 -35 =0

Let x^-1 =y

y^2 -2y -35 =0

y^2 -7y +5y -35 =0

y( y-7) + 5( y-7) =0

(y+5)(y-7) =0

y =-5 ----> x^-1 = -5

x = -1/5

y =7 ---> x^-1 =7

x = 1/7