Question

1/4x + 3 > -10

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we need to isolate the variable x.

1/4x + 3 > -10

First, subtract 3 from both sides of the inequality:

1/4x > -13

Next, multiply both sides of the inequality by 4 to eliminate the fraction:

4 * (1/4x) > 4 * (-13)

x > -52

Therefore, the solution to the inequality is x > -52.

Answer 2

graph this inequality:

Answer 3

[AI-generated answer — Bot GPT 3.5]

To graph the inequality 1/4x + 3 > -10, we can start by graphing the line 1/4x + 3 = -10, which is the boundary line for the inequality.

To graph the line 1/4x + 3 = -10, we can rearrange it as follows:

1/4x = -13

x = -13 * 4

x = -52

Therefore, the boundary line is x = -52, which is a vertical line passing through -52 on the x-axis.

Next, we need to determine whether to shade the region above or below the line. To do this, we can choose a test point in either region and substitute it into the inequality.

For example, let's test the point (0,0):

1/4 * 0 + 3 > -10

0 + 3 > -10

3 > -10

Since 3 is indeed greater than -10, this means that the region containing the point (0,0) satisfies the inequality. Thus, we should shade the region above the line x = -52.

So, the graph of the inequality 1/4x + 3 > -10 is a vertical line passing through x = -52 on the x-axis, with the region above the line shaded.

Answer 4

[AI-generated answer — Explain Bot]

To solve the inequality "1/4x + 3 > -10," we can follow these steps:

Step 1: Start by subtracting 3 from both sides of the inequality to get rid of the constant term on the left side.
(1/4x + 3) - 3 > -10 - 3
1/4x > -13

Step 2: Next, we need to isolate x by multiplying both sides of the inequality by 4. This is done to cancel out the coefficient (1/4) on the left side.
4 * (1/4x) > 4 * (-13)
x > -52

Step 3: Finally, the solution to the inequality is x > -52.

Therefore, any value of x that is greater than -52 will make the inequality 1/4x + 3 > -10 true.