Answer:
A number line with a point at 3 with a bold line pointing to the right stopping at the open circle at 5.
Step-by-step explanation:
Phyllis solved the compound inequality [tex]16\le2(3x-1) < 28.[/tex] She began by first breaking the inequality into two separate inequalities [tex]16\le 2(3x-1)[/tex] and [tex]2(3x-1)<28[/tex], then she correctly solved each for x:
1) [tex]16\le 2(3x-1):[/tex]
Rewrite this inequality:
[tex]2(3x-1)\ge 16[/tex]
Divide by 2:
[tex]3x-1\ge 8[/tex]
Add 1:
[tex]3x-1+1\ge 8+1\\ \\3x\ge 9[/tex]
Divide by 3:
[tex]x\ge 3[/tex]
2) [tex]2(3x-1)<28:[/tex]
Divide by 2:
[tex]3x-1<14[/tex]
Add 1:
[tex]3x-1+1<14+1\\ \\3x<15[/tex]
Divide by 3:
[tex]x<5[/tex]
The solution to the compound inequality are all values of x which are greater than 3 or equal to 3 and less than 5. So, you have to plot point at 3, draw a bold line to 5 and plot open circle at 5. Hence, option
A number line with a point at 3 with a bold line pointing to the right stopping at the open circle at 5
is true.
The answer to your question would be A.
Hope you have a nice day!
