Answer
$\{t\ |\ t\geq-2.\overline3\}\cap\{t\ |\ t\leq3\}$
Work Step by Step
$|4.5t-1.5|\leq12\longrightarrow$ write and solve a compound inequality
$-12\leq4.5t-1.5\leq12\longrightarrow$ add 1.5 to each part
$-12+1.5\leq4.5t-1.5+1.5\leq12+1.5\longrightarrow$ add
$-10.5\leq4.5t\leq13.5\longrightarrow$ divide each part by 4.5
$-10.5\div4.5\leq4.5t\div4.5\leq13.5\div4.5\longrightarrow$ divide
$-2.\overline3\leq t\leq3$
This compound inequality can be rewritten as
$t\geq-2.\overline3$ AND $t\leq3$
A compound inequality joined by AND can be written as the intersection of 2 sets.
