'gtk/gtk.h' file not found Even with pkg-config - c

Question

I'm creating a software in C using the SDL library and GTK+3. My first attempt with GTK+3 on a specific main.c and its Makefile works well, but when I try to add my GTK project to the other piece of code using my "real" Makefile, even if I added the same flags for GTK+3, I can't compile and get the gtk/gtk.h file no found error. I visited many threads about this error but I still can't make it work.
Here's my old Makefile, making things work:
CC=clang
CPPFLAGS= `pkg-config --cflags gtk+-3.0`
CFLAGS= -Wall -Wextra -std=c99 -O2
LDFLAGS=
LDLIBS= `pkg-config --libs gtk+-3.0` `pkg-config gmodule-2.0 --libs`
SRC= main.c
OBJ= ${SRC:.c=.o}
all: main
main: ${OBJ} -lm
clean:
rm -f *~ *.o main
And here's the one I use for the project:
CC=clang
CPPFLAGS= `pkg-config --cflags sdl gtk+-3.0`
CFLAGS= -Wall -Wextra -Werror -std=c99 -O2 -pedantic
LDFLAGS=
LDLIBS= `pkg-config --libs sdl` `pkg-config --libs gtk+-3.0` `pkg-config gmodule-2.0 --libs` -lgtk -lgdk -lglib -lX11 -lXext -lSDL -lSDL_image -lm
SRCDIR = src
OBJDIR = obj
BINDIR = bin
TARGET = main
SOURCES := $(wildcard $(SRCDIR)/*.c)
INCLUDES := $(wildcard $(SRCDIR)/*.h)
DEPENDS := $(wildcard $(OBJDIR)/*.d)
OBJECTS := $(SOURCES:$(SRCDIR)/%.c=$(OBJDIR)/%.o)
rm = rm -f
all: makedirs $(BINDIR)/$(TARGET)
$(BINDIR)/$(TARGET): $(OBJECTS)
#$(CC) $(OBJECTS) $(LDLIBS) -o $#
#echo "Linking complete!"
$(OBJECTS): $(OBJDIR)/%.o : $(SRCDIR)/%.c
#$(CC) $(CFLAGS) -c $< -o $#
#echo "[OK] Compiled "$<""
makedirs:
#mkdir -p $(OBJDIR)
#mkdir -p $(BINDIR)
#echo "[OK] Created directories : $(BINDIR) $(OBJDIR)"
[....] etc
And the error:
src/main.c:2:14: fatal error: 'gtk/gtk.h' file not found
#include <gtk/gtk.h>
Tanks for the attention :)
[EDIT]
~
▶ pkg-config --libs gtk+-3.0
-lgtk-3 -lgdk-3 -lpangocairo-1.0 -lpango-1.0 -latk-1.0 -lcairo-gobject -lcairo -lgdk_pixbuf-2.0 -lgio-2.0 -lgobject-2.0 -lglib-2.0
~
▶ pkg-config --cflags sdl gtk+-3.0
-D_GNU_SOURCE=1 -D_REENTRANT -pthread -I/usr/include/SDL -I/usr/include/gtk-3.0 -I/usr/include/at-spi2-atk/2.0 -I/usr/include/at-spi-2.0 -I/usr/include/dbus-1.0 -I/usr/lib/x86_64-linux-gnu/dbus-1.0/include -I/usr/include/gtk-3.0 -I/usr/include/gio-unix-2.0/ -I/usr/include/cairo -I/usr/include/pango-1.0 -I/usr/include/harfbuzz -I/usr/include/pango-1.0 -I/usr/include/atk-1.0 -I/usr/include/cairo -I/usr/include/pixman-1 -I/usr/include/freetype2 -I/usr/include/libpng12 -I/usr/include/gdk-pixbuf-2.0 -I/usr/include/libpng12 -I/usr/include/glib-2.0 -I/usr/lib/x86_64-linux-gnu/glib-2.0/include
And the header of main.c:
#include <gtk/gtk.h>
#include <stdio.h>
#include <stdlib.h>
#include "neural.h"

Answer 1

As Y. Verzun said, I forgot to add the CPPFLAGS rule, but not only to the OBJECTS:
$(BINDIR)/$(TARGET): $(OBJECTS)
#$(CC) $(OBJECTS) $(LDLIBS) $(CPPFLAGS) -o $#
#echo "Linking complete!"
$(OBJECTS): $(OBJDIR)/%.o : $(SRCDIR)/%.c
#$(CC) $(CFLAGS) $(CPPFLAGS) -c $< -o $#
#echo "[OK] Compiled "$<""
here's the code working, notice both of the $(CPPFLAGS) added.
Thanks a lot !

Answer 2

You simply forgot to add CPPFLAGS to the rule $(OBJECTS)
It should look like:
$(OBJECTS): $(OBJDIR)/%.o :
$(SRCDIR)/%.c#$(CC) $(CFLAGS) $(CPPFLAGS) -c $< -o $#
#echo "[OK] Compiled "$<""