How do you solve #- 5abs(x + 1)= -10#?

x= 1, -3

The expression inside the absolute will sign may either be a positive or a negative number. Hence, if the absolute value sign is disregarded, the expression may be considered firstly as positive and next as negative, giving rise two two equations.

First consider x+1 being positive, then -5(x+1)= -10. On solving this it would come out to be x=1

Next consider x+1 being negative, then in that case 5(x+1)= -10. On solving this it would come out to be x= -3

To solve the equation ( -5| x + 1 | = -10 ), you first isolate the absolute value expression by dividing both sides by -5:

[ | x + 1 | = \frac{-10}{-5} = 2 ]

Then, you consider the two possible cases:

1. When ( x + 1 ) is positive: [ x + 1 = 2 ] [ x = 2 - 1 ] [ x = 1 ]

2. When ( x + 1 ) is negative: [ -(x + 1) = 2 ] [ -x - 1 = 2 ] [ -x = 2 + 1 ] [ -x = 3 ] [ x = -3 ]

So, the solutions to the equation are ( x = 1 ) and ( x = -3 ).