Given the above graph, we can initially deduce that , , and  are not the correct answer. The dashed line in the graph indicates that no point on the line  is a solution to the inequality, and the shaded area indicates that the correct answer must account for points in a certain region beyond . Thus, we're left with  and .

We can use a test point to determine which of the remaining inequalities is the correct answer. The test point can be any point that is not on the line, so let's select  in this case. Plugging  into  yields . Since this is true, we know that every point on the same side of the line as  will yield a true result, and that our graph represents .

Given the above graph, we can initially deduce that , , and  are not the correct answer. The dashed line in the graph indicates that no point on the line  is a solution to the inequality, and the shaded area indicates that the correct answer must account for points in a certain region beyond . Thus, we're left with  and .

We can use a test point to determine which of the remaining inequalities is the correct answer. The test point can be any point that is not on the line, so let's select  in this case. Plugging  into  yields . Since this is true, we know that every point on the same side of the line as  will yield a true result, and that our graph represents .

Given the above graph, we can initially deduce that , , and  are not the correct answer. The solid line in the graph indicates that all points on the line   are solutions to the inequality, and the shaded area indicates that the correct answer must account for points in a certain region beyond . Thus, we're left with  and .

We can use a test point to determine which of the remaining inequalities is the correct answer. The test point can be any point that is not on the line, so let's select  in this case. Plugging  into  yields . Since this is true, we know that every point on the same side of the line as  will yield a true result, and that our graph represents .

Given the above graph, we can initially deduce that , , and  are not the correct answer. The solid line in the graph indicates that all points on the line   are solutions to the inequality, and the shaded area indicates that the correct answer must account for points in a certain region beyond . Thus, we're left with  and .

We can use a test point to determine which of the remaining inequalities is the correct answer. The test point can be any point that is not on the line, so let's select  in this case. Plugging  into  yields . Since this is true, we know that every point on the same side of the line as  will yield a true result, and that our graph represents .

Because the line is a solid line and is shaded down you know that the equation is less than or equal to some function.

When finding slope, you must find the rise over the run which is 2. The function also has a y-intercept of 7,

So your end result of your equation is:

Let's start by looking at the given equation:

The inequality is written in slope-intercept form; therefore, the slope is equal to  and the y-intercept is equal to .

All of the graphs depict a line with slope of  and y-intercept . Next, we need to decide if we should shade above or below the line. To do this, we can determine if the statement is true using the origin . If the origin satisfies the inequality, we will know to shade below the line. Substitute the values into the given equation and solve.

Because this statement is true, the origin must be included in the shaded region, so we shade below the line.

Finally, a statement that is "less than" or "greater than" requires a dashed line in the graph. On the other hand, those that are "greater than or equal to" or "less than or equal to" require a solid line. We will select the graph with shading below a dashed line.

The absolute value of a number must always be nonnegative, so   can never be less than . This means the inequality has no solution.

First, we can simplify this inequality by subtracting 7 from both sides. This gives us 

Next, however, we need to make two separate inequalities due to the presence of an absolute value expression. What this inequality actually means is that 

and 

(Be careful with the inequality signs here! The second sign must be switched to allow for the effect of absolute value on negative numbers. In other words, the inequality must be greater than  because, after the absolute value is applied, it will be less than 7.) When we solve the two inequalities, we get two solutions: 

and 

For the original statement to be true, both of these inequalities must be fulfilled. We're left with a final answer of 

The inequality compares an absolute value function with a negative integer. Since the absolute value of any real number is greater than or equal to 0, it can never be less than a negative number. Therefore,  can never happen. There is no solution. 

Split the inequality into two possible cases as follows, based on the absolute values.

First case:

Second case: 

Let's find the inequality of the first case.

Multiply both sides by x + 6.

Subtract x from both sides, then subtract 3 from both sides.

Divide both sides by 3.

Let's find the inequality of the second case.

Multiply both sides by x + 6.

Simplify.

Add x to both sides, then subtract 3 from both sides.

Divide both sides by 5.

So the range of x-values is   and  .