Select the graph that would represent the best presentation of the solution set.
|1 - 4x| > 7
The correct graph to represent the solution set is a graph with two lines, one above the other, with a shaded region between them. The lines represent the inequality |1 - 4x| > 7.
To graph the solution set for the inequality |1 - 4x| > 7, we need to consider two cases:
Case 1: 1 - 4x > 7
Solving this case, we have:
1 - 4x > 7
-4x > 7 - 1
-4x > 6
x < -6/4
x < -3/2
Case 2: -(1 - 4x) > 7
Solving this case, we have:
-(1 - 4x) > 7
-1 + 4x > 7
4x > 7 + 1
4x > 8
x > 8/4
x > 2
Therefore, the graph that would represent the best presentation of the solution set would be a number line with an open circle at -3/2 (indicating that x is less than -3/2) and a shaded region to the right of 2 (indicating that x is greater than 2).
To find the best representation of the solution set for the inequality |1 - 4x| > 7, we need to understand the components of the inequality and how to approach graphing it.
First, let's break down the inequality. The absolute value of the expression 1 - 4x is greater than 7. This means that either (1 - 4x) is greater than 7 or it is less than -7.
So, we have two inequalities to consider:
1 - 4x > 7 or 1 - 4x < -7
To find the solution set for the first inequality, let's solve for x:
1 - 4x > 7
Subtracting 1 from both sides:
-4x > 6
Dividing both sides by -4 (remember to flip the inequality sign when dividing by a negative number):
x < -6/4 or x < -3/2
Now, let's find the solution set for the second inequality:
1 - 4x < -7
Subtracting 1 from both sides:
-4x < -8
Dividing both sides by -4 (again, remember to flip the inequality sign):
x > 2
So, we have x < -3/2 or x > 2 as the two parts of the solution set.
Now, let's look at the graph options. We need to choose the graph that correctly represents the solution set.
Graph Option 1: Graph Option 2: Graph Option 3: Graph Option 4:
[]------------------] []-----------[...] [....-----------[] ]-----------------[]
-3/2 2
Graph Option 1 represents all the values less than -3/2 and all the values greater than 2 as the solution set. This is the correct graph for the given inequality and the best presentation of the solution set.
Therefore, the answer is Graph Option 1.