מתמטיקה תיכונית/פתרונות לספרים/מתמטיקה (5 יחידות לימוד) חלק ו' שאלון 035006/עמוד 74 סעיף 32

$\ 2<|3x+1|\leq 7$
$\color {blue}2<|3x+1|$			$\ and$	$\color {red}|3x+1|<7$
${\begin{aligned}&\color {SkyBlue}2<3x+1\\&\color {SkyBlue}3x>1\\&\color {SkyBlue}x>{\frac {1}{3}}\\\end{aligned}}$	$\ ;$	${\begin{aligned}&\color {NavyBlue}-2>3x+1\\&\color {NavyBlue}3x<-3\\&\color {NavyBlue}x<-1\\\end{aligned}}$		$\color {Red}-7\leq 3x+1\leq 7$
$\color {blue}x>{\frac {1}{3}};x<-1$				${\begin{aligned}&\color {OrangeRed}-7\leq 3x+1\\&\color {OrangeRed}3x\geq -8\\&\color {OrangeRed}x\geq -2{\frac {2}{3}}\\\end{aligned}}$	$\ and$	${\begin{aligned}&\color {BrickRed}3x+1\leq 7\\&\color {BrickRed}3x\leq 6\\&\color {BrickRed}x\leq 2\\\end{aligned}}$
				$\color {red}-2{\frac {2}{3}}\leq x\leq 2$
$\ -2{\frac {2}{3}}\leq x<-1;{\frac {1}{3}}<x\leq 2$