Answer: [tex]0\leq x<4[/tex]
Step-by-step explanation:
The inequality could be broken into two:
[tex]-2\leq 3x-2[/tex] .......................... 1
[tex]3x-2<10[/tex] ......................... 2
solving equation 1
[tex]-2\leq 3x-2[/tex]
add 2 to both sides , we have
[tex]-2+2\leq 3x[/tex]
[tex]0\leq 3x[/tex]
divide through by 3 , we have
[tex]0\leq x[/tex]
solving equation 2
[tex]3x-2<10[/tex]
add 2 to both sides, we have
[tex]3x < 10 + 2[/tex]
[tex]3x < 12[/tex]
divide through by 3
[tex]x<4[/tex]
combining the two answers , we have
[tex]0\leq x<4[/tex]
