Question

#HP Help.Please

Which graph represents the solution set of this inequality? \qquad12b - 15 > 2112b−15>2112, b, minus, 15, is greater than, 21 Choose 1 answer: Choose 1 answer: (Choice A) A (Choice B) B (Choice C) C (Choice D) D

Answer 1

This answers to equals to 21

Answer 2

The correct option is D.

To solve the inequality
`\( 12b - 15 > 2112 \)`, we follow these steps:

1. Add 15 to both sides of the inequality to isolate the term with b :

`\( 12b > 2112 + 15 \)`

2. Simplify the right side:

`\( 12b > 2127 \)`

3. Divide both sides by 12 to solve for b :

`\( b > (2127)/(12) \)`

4. Simplify the fraction
`\( (2127)/(12) \)` to get the boundary of the inequality.

The simplified boundary for b is
`\(b > (709)/(4) \).` The inequality indicates that b can be any number greater than
`\( (709)/(4) \),` which is approximately 177.25.

Now, let's match this solution to the correct graph:

- Graph A (blue arrow) shows all numbers less than a certain value, which does not match our solution.

- Graph B (green arrow) shows all numbers greater than a certain value, including that value (as indicated by the filled-in circle).

- Graph C (pink arrow) shows all numbers less than a certain value and includes that value.

- Graph D (red arrow) shows all numbers greater than a certain value but does not include that value (as indicated by the open circle).

Since we are looking for all numbers greater than
`\( (709)/(4) \)` and the inequality does not include the equality
`( \( b > (709)/(4) \)` not
`\( b \geq (709)/(4) \))`, the correct graph is the one with an open circle indicating that the value
`\( (709)/(4) \)`is not included in the solution set.