math help

Question

solve  |x-1|+|x+5|=6 algebraically

Answer 1

The absolute value equation is |x - 1| + | x + 5| = 6.

Case 1 : (x - 1) + (x + 5) = 6.

x - 1 + x + 5 = 6

2x + 4 = 6

2x = 6 - 4

2x = 2

x=  2/2

x = 1.

Case 2 : - (x - 1) + [ - (x + 5) ] = 6.

- x + 1 - x - 5 = 6

- 2x - 4 = 6

- 2x = 6 + 4

- 2x = 10

x=  10/(- 2)

x = - 5.

Case 3 : - (x - 1) + (x + 5) = 6.

- x + 1 + x + 5 = 6

6 = 6.

The above statement is true and there is no solution for x.

Case 4 : (x - 1) - (x + 5) = 6.

x - 1 - x - 5 = 6

- 6 = 6

The above statement is false and there is no solution for x.

So, the solutions of the given absolute value equation are x = - 5 and x = 1.