How to install MODX on lamp, why does it give directory write errors?

Question

MODX

Good day!
There was a problem installing MODX 2.4.4 on lamp in Virtualbox.
I installed it on Debian 8, set up lamp, uploaded MODX to the server, followed the instructions from Rosehosting , went to the setup folder, started installing, and at the last stage, the deadlines give errors:
Checking the ability to write to the /var/www/modx/ directory: Error!
Checking whether /var/www/modx/back/ is writable: Error!
Checking whether /var/www/modx/connectors/ is writable: Error!
Help me to understand!
my commands during installation:
install lamp
apt-get update
apt-get install apache2 mysql-server libapache2-mod-auth-mysql php5-mysql mysql_install_db php5 libapache2-mod-php5 php5-mcrypt
nano /etc/apache2/mods-enabled/dir.conf (checked for index.php)
install MODX -advanced:
downloaded and unpacked MODX in /var/www/, renamed the folder,
nano /etc/php5/apache2/php.ini set timezone in the file, default php 128 mb,
service apache2 restart
apt-get update
apt-get install php5-gd install imagemagick
a2enmod rewrite set entry to apache2
nano /etc/apache2/sites-available/000-default.conf in documentroot set folder /var/www/
nano /etc/apache2/apache2.conf to
Directory /var/www /
Options Indexes FollowSymLinks
AllowOverride All
Require all granted
/Directory set All instead of None
service apache2 restart
set folder
permissions chown -R root:www-data core/cache
chown -R root:www-data core/config
chown -R root:www-data core/ export
chown -R root:www-data core/packages
chmod -R 775 core/cache
chmod -R 775 core/config
chmod -R 775 core/export
chmod -R 775 core/packages
created database create database modx;
service apache2 restart
I noticed that the instructions need to edit the /etc/apache2/sites-available/default file, but it is not in the latest version of apache2, I edited /etc/apache2/apache2.conf

Answer 1

I tried not to set permissions, gave an error:
CRITICAL ERROR: MODX installation cannot be continued.
Make sure the /var/www/modx/core/cache directory exists and is writable by PHP processes.
installed from under root.
I had to give the rights, but the recording errors remained.
The problem was solved by adding permissions to the modx folder:
cd /var/
chown -R root:www-data www/modx
chmod -R 775 www/modx

Answer 2

For a long time already I wrote 2 instructions for setting up an Nginx + PHP-FPM + MySQL server:
The first one is probably already outdated. And the second , even with video.
Tried many times, works 100%.

Answer 3

If the web server user can write to these directories, you need to take away the rights