##DESCRIPTION
## Absolute Value Equalites and Inequalities
## 
##ENDDESCRIPTION
## DBsubject(Algebra)
## DBchapter(Inequalities and problem solving)
## DBsection('Equations and Inequalities Involving Absolute Value')
## KEYWORDS('inequalities','absolute value')
## TitleText1('Essentials of Intermediate Algebra')
## EditionText1('1')
## AuthorText1('Blitzer')
## Section1('4.3
## Problem1('')
## Author('RA Cruz')
## Institution('The College of Idaho')
## Date: 2007/10

DOCUMENT(); # This should be the first executable line in the problem.

loadMacros(
  "PGstandard.pl",
  "MathObjects.pl",
  "contextInequalitiesAllowStrings.pl",
);

TEXT(beginproblem());

######################################
#  Setup

Context("Inequalities-AllowStrings");
Context()->constants->add(a => Real(exp(2)/cos(3)), b=> Real(3147.115));
Context()->flags->set(formatStudentAnswers=>"parsed");
Context()->strings->add(none=>{});

$c = random(-10,10,1);

Context()->texStrings;
######################################

#  Main text


BEGIN_TEXT
Solve for \(x\) in terms of \(a\) and \(b\) (you may assume \(a \gt 0\)):  \( |a x + b| \le $c \)
$PAR
Answer:  \{ ans_rule(20) \}
$BR
Note: 
END_TEXT


######################################
Context()->normalStrings;
#  Answer


$ans = Compute("0");
if($c < 0 )
{  $ans = Compute("none"); }
if($c==0)
{ $ans = Compute("x=-b/a"); }
if($c>0)
{ $ans = Compute("(-$c-b)/a<=x<=($c-b)/a"); }
ANS($ans->cmp); 

$showPartialCorrectAnswers = 1;

######################################


COMMENT('MathObject version');
ENDDOCUMENT();