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correct answer is infinitely many solutions

step-by-step explanation:

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

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions

we have been given a piecewise function which has three parts

we can graph each part one by one.

first part is x+1 which is just like equation y=x+1

restriction with first part is x< 0 so that means we can use any number for x which is less than 0 for example x=-1 and x=-2

now plug x=-1 into y=x+1 to get y

y=x+1=-1+1=0

so the point will be (-1,0)

similarly we get another point (-2,-1)

now we graph a line joining both points but keep in mind that line must be on left side of x=0 because of restriction x< 0

same way we can graph 2nd and third parts

if we have < or > then we use open circle.

if we have < = or > = then we use close circle.

so using above information, final graph can be drawn as: