Match the inequality to its graphed solution.(2 points)

Question

Match the inequality to its graphed solution.(2 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. The option "$8x < 4x+28$" (3 of 4) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel. 1. 1over4 (8x + 16)> -4 2. -3(x- 12)>0 3. 8x < 4x + 28 4. -5 (x+5)> - 15

GPT-4o mini · Answer

To match the inequality with its graphed solution, let's analyze each given option:

$ \frac{1}{4}(8x + 16) > -4 $
- This simplifies to $ 8x + 16 > -16 $ or $ 8x > -32 $, leading to $ x > -4 $.
$-3(x - 12) > 0$
- This simplifies to $ -3x + 36 > 0 $ or $ -3x > -36 $, leading to $ x < 12 $.
$ 8x < 4x + 28 $
- This simplifies to $ 4x < 28 $, leading to $ x < 7 $.
$-5(x + 5) > -15$
- This simplifies to $ -5x - 25 > -15 $ or $ -5x > 10 $, leading to $ x < -2 $.

Now, let's summarize:

Option 1: $ x > -4 $
Option 2: $ x < 12 $
Option 3: $ x < 7 $
Option 4: $ x < -2 $

To match them to their graphed solutions, you should align them based on the ranges indicated:

$ \frac{1}{4}(8x + 16) > -4 $ is typically represented with an open line to the right.
$-3(x - 12) > 0$ is represented with an open line to the left that stops before 12.
$ 8x < 4x + 28$ is similar to an open line to the left that bounds at 7.
$-5(x + 5) > -15$ is represented with an open line to the left that stops before -2.

Thus, the response for $8x < 4x + 28$ is 3.

The final match will look like this:

$3$ for $8x < 4x + 28$
$1$ for $ \frac{1}{4}(8x + 16) > -4 $
$2$ for $-3(x - 12) > 0$
$4$ for $-5(x + 5) > -15$

These inequalities would then be matched to their respective graphed solutions based on the corresponding ranges. Please input as specified in the question.