Question

Phyllis solved the compound inequality 16 ≤ 2(3x – 1) < 28. She began by first breaking the inequality into two separate inequalities, then she correctly solved each for x. Which graph represents her solution? A number line with a point at 3 with a bold line pointing to the right stopping at the open circle at 5. A number line with an open circle at 3 with a bold line pointing to the right stopping at the point 5. A number line with a point at 3 with a bold line pointing to the left and an open circle at 5 with a bold line pointing to the right. A number line with an open circle at 3 with a bold line pointing to the left and a point at 5 with a bold line pointing to the right.

Answer 1

The answer to your question would be A.

Hope you have a nice day!

Answer 2

A number line with a point at 3 with a bold line pointing to the right stopping at the open circle at 5.

Explanation:

Phyllis solved the compound inequality
`16\le2(3x-1) < 28.` She began by first breaking the inequality into two separate inequalities
`16\le 2(3x-1)` and
`2(3x-1)<28`, then she correctly solved each for x:

1)
`16\le 2(3x-1):`

Rewrite this inequality:

`2(3x-1)\ge 16`

Divide by 2:

`3x-1\ge 8`

Add 1:

`3x-1+1\ge 8+1\\ \\3x\ge 9`

Divide by 3:

`x\ge 3`

2)
`2(3x-1)<28:`

Divide by 2:

`3x-1<14`

Add 1:

`3x-1+1<14+1\\ \\3x<15`

Divide by 3:

`x<5`

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.