solve and graph the following inequality. -8p-5<-13
Can someone please help me solve this because i tried it but im not quite sure if i solved it right.
Woahhh this was from 2009…looks like nobody help u out lol
To solve the inequality -8p - 5 < -13, follow these steps:
Step 1: Add 5 to both sides of the inequality to isolate the variable term (-8p) on the left side:
-8p - 5 +5 < -13 + 5
-8p < -8
Step 2: Divide both sides of the inequality by -8. Remember that when dividing by a negative number, you need to flip the inequality sign:
(-8p) / (-8) > (-8) / (-8)
p > 1
So the solution to the inequality is p > 1.
To graph this inequality on a number line, follow these steps:
Step 1: Draw a number line and mark a point at 1.
Step 2: Since the inequality is p > 1, you need to indicate that the point 1 is not part of the solution. You can do this by making an open circle at 1 instead of a filled-in circle.
Step 3: Shade the region to the right of 1 to represent all the values greater than 1.
Your graph should have an open circle at 1 and be shaded to the right of 1.
To solve the inequality -8p - 5 < -13, you can follow these steps:
Step 1: Begin by isolating the variable p on one side of the inequality.
-8p - 5 < -13
Subtract -5 from both sides:
-8p - 5 + 5 < -13 - 5
-8p < -18
Step 2: To further isolate p, divide both sides of the inequality by the coefficient of p, which is -8. Remember, when you divide an inequality by a negative number, you must flip the direction of the inequality.
-8p < -18
Divide by -8 (and flip the inequality sign):
-8p / -8 > -18 / -8
p > 18/8
Simplify the right side:
p > 9/4
Step 3: The solution is p > 9/4 or p > 2.25. This means that p must be greater than 2.25 but can be any value after 2.25.
Now, let's graph the solution on a number line:
1. Mark a point on the number line at 2.25. Since p is greater than 2.25, the point should be an open circle.
┘
---------------- . (2.25)
2. Draw an arrow to the right of the point to represent all values greater than p = 2.25.
┘
----------------------------->
p
This graph visually represents all values of p that make the inequality -8p - 5 < -13 true.