Problem with Arduino recognizing an added library

I'm working from a backpack produced by adafruit, and trying to compile just to make sure I've got all my ducks in a row.

sample of code with the problem section

#include <Wire.h> // Enable this line if using Arduino Uno, Mega, etc.
//#include <TinyWireM.h> // Enable this line if using Adafruit Trinket, Gemma, etc.

#include "Adafruit_LEDBackpack.h"
#include "Adafruit_GFX.h"

Adafruit_7segment matrix = Adafruit_7segment();

void setup() {
#ifndef __AVR_ATtiny85__
  Serial.begin(9600);
  Serial.println("7 Segment Backpack Test");
#endif
  matrix.begin(0x70);
}

When I try to compile it, I get, among other things, the following error.

sevenseg.ino:28:34: error: Adafruit_LEDBackpack.h: No such file or directory

I have tried closing and restarting after adding the libraries, and I have tried deleting the libraries from arduino and adding them in from someplace else. And I'm not sure what else I can try.

Screenshot attached (for proof that I have added these libraries)

any advice would be greatly appreciated.

When you add a library using the Arduino IDE, they are located in the "libraries" folder in your project folder.
You have to include them with '<' and '>', because they are libraries.
When you include with double quotes ("), the Arduino IDE looks for them in local files.

So I think you have include the Adafruit libraries using '<' and '>'.
#include <Adafruit_LEDBackpack.h>