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

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 $16\le2(3x-1) < 28.$ She began by first breaking the inequality into two separate inequalities $16\le 2(3x-1)$ and $2(3x-1)$, 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) $2(3x-1)$

Divide by 2:

$3x-1$

Add 1:

$3x-1+1$

Divide by 3:

$x$

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.

Answer 2

The answer to your question would be A.  

Hope you have a nice day!