Please help.

choose the definition for the function.

All four answer choices have an "x+1" and "x+2" as part of the piecewise definition. The only differences are that the inequalities are set up slightly different from one another. The inequalities determine which equation is graphed.

The left part of the piece-wise graph given is the equation y = x+1 but only when x is 2 or smaller. So only when . Note the closed or filled in circle at the endpoint for this left piece.

The right piece has an open circle meaning we do not include x = 2 here. So we go with x > 2 instead of

Choices C and D are not possible because x = 2 would lead to more than one output. In other words, we wouldn't have a function here since it fails the vertical line test. Choice B would only be valid if the open and closed endpoints were swapped.

step-by-step explanation:

subtract 7, so the answer is x < = 3, or c.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.