Solve the compound inequality. Graph the solutions.
13<4p-3<25
To solve the compound inequality, we will solve each inequality separately and then combine the solutions.
First inequality:
13 < 4p - 3
Adding 3 to both sides:
16 < 4p
Dividing both sides by 4:
4 < p
Second inequality:
4p - 3 < 25
Adding 3 to both sides:
4p < 28
Dividing both sides by 4:
p < 7
Combining the solutions:
The solution to the compound inequality is 4 < p < 7.
To graph the solution, we can use an open circle at 4 and an open circle at 7 on a number line, then shade the region between them.
To solve the compound inequality 13 < 4p - 3 < 25, we will break it down into two separate inequalities and solve each one individually.
1. 13 < 4p - 3:
Add 3 to both sides of the inequality to isolate the variable term:
13 + 3 < 4p - 3 + 3
16 < 4p
Divide both sides of the inequality by 4 to solve for p:
16/4 < 4p/4
4 < p
2. 4p - 3 < 25:
Add 3 to both sides of the inequality to isolate the variable term:
4p - 3 + 3 < 25 + 3
4p < 28
Divide both sides of the inequality by 4 to solve for p:
4p/4 < 28/4
p < 7
Therefore, the solution to the compound inequality 13 < 4p - 3 < 25 is 4 < p < 7.
To graph the solutions, we can represent them on a number line:
-----4----7-----------------
So, the solutions are all values of p between 4 and 7, excluding the endpoints.
To solve the compound inequality 13 < 4p - 3 < 25, we will break it down into two separate inequalities and solve each one individually.
First, let's solve the left inequality:
13 < 4p - 3
First, add 3 to both sides of the inequality to isolate the variable:
13 + 3 < 4p - 3 + 3
16 < 4p
Next, divide both sides of the inequality by 4 to solve for p:
16/4 < 4p/4
4 < p
Now, let's solve the right inequality:
4p - 3 < 25
First, add 3 to both sides of the inequality to isolate the variable:
4p - 3 + 3 < 25 + 3
4p < 28
Next, divide both sides of the inequality by 4 to solve for p:
4p/4 < 28/4
p < 7
Therefore, the solution to the compound inequality 13 < 4p - 3 < 25 is 4 < p < 7.
To graph the solution on a number line, draw a line with a closed circle on 4 and an open circle on 7. Shade the region between these two points to represent the solution set.