Y + 4 ≤ |x-2| please explain how to solve and graph it. Also please show a graph.
| = an absolute value bar, it kinda looks like 1

Step-by-step explanation:

y ≤ |x - 2| + 4

Step-by-step explanation:

step (1)

move the 4 to the other side, so it would look like:

y≤ |x-2| + 4

step (2)

now we can start graphing it, you would first start on the x axis moving it to the right. so your point on the graph should be (2,0) {don't graph a point there though}

the reason we do this is because the absolute value means the opposite so everytime there is a number in the absolute value being added or subtracted by just x then we move it the opposite side.

then from that (2,0) we go up four which would now make it (2,4). that is our first point and vertex so graph that.

now in y≤ |x-2| +4 you have to note that if there is nothing next to the equality and the absolute value, then it will become a 1. so our equation will now look like y ≤ 1 |x-2| + 4. so with that from our (2,4) point, we go up one and to the right one and to the left one. So there should be two more points at (3, 5) and (1, 5).

we then keep following the pattern of going up one and the right one and to the left one. the graph line should be in a V shape.

step (3)

now there is one last thing you need to do which is shading. what you're going to do first is check the inequality sign. if the inequality sign has a line under it (meaning equal to) then the line will be a solid line. if it doesn't then there should be a dashed line. our inequality sign has a line under it so it is a solid line.

then we need to figure out where to shade, above or below. if the y is greater than the rest of the equation then that means you need to shade above the V shape. however, if it were to be less than the rest of the equation you would shade below the V shape.

in this problem since the y is less than the rest of the equation, shade downwards.

i hope this answered your question and sorry if my explanation was hard to understand, its a pretty lengthy and confusing but it was the only way i knew of how to explain :))

the answer is b.)

< 1=< 2