ACTIVITY SOLVE ANG GRAPH THE SOLUTION SET.(EXCEPT 2) 1) 4x+5-15 or 6x-11>7 2) Joe earned scores of 72,85, and 75 on his first three algebra exams. What must he score on the fourth exam to average at least 80? 3) If five is added to three times a number, then the result is less than twenty.
Answers & Comments
Verified answer
4x+5-15 or 6x-11>7For the first inequality, we have:
4x + 5 ≤ 15
Subtracting 5 from both sides, we get:
4x ≤ 10
Dividing by 4 (and remembering to flip the inequality sign, since we're dividing by a negative number), we get:
x ≤ 2.5
So the solution set for this inequality is x ≤ 2.5.
For the second inequality, we have:
6x - 11 > 7
Adding 11 to both sides, we get:
6x > 18
Dividing by 6, we get:
x > 3
So the solution set for this inequality is x > 3.
Therefore, the solution set for the entire inequality is x > 3 OR x ≤ 2.5.
We can graph this on a number line as follows:
----o----------------o-----------------o------
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
The open circles indicate that the endpoints (2.5 and 3) are not included in the solution set.
Joe earned scores of 72, 85, and 75 on his first three algebra exams. What must he score on the fourth exam to average at least 80?
Let x be the score Joe must earn on the fourth exam. Then the average of his four scores will be:
(72 + 85 + 75 + x)/4
We want this average to be at least 80, so we can write:
(72 + 85 + 75 + x)/4 ≥ 80
Multiplying both sides by 4, we get:
72 + 85 + 75 + x ≥ 320
Adding the numbers on the left side, we get:
232 + x ≥ 320
Subtracting 232 from both sides, we get:
x ≥ 88
So Joe must earn a score of at least 88 on the fourth exam to average at least 80.
If five is added to three times a number, then the result is less than twenty.
Let x be the number we're trying to find. Then we can write:
3x + 5 < 20
Subtracting 5 from both sides, we get:
3x < 15
Dividing by 3, we get:
x < 5
So the solution set for this inequality is x < 5.
We can graph this on a number line as follows:
-----o----------------o-----------------o------
-4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
The open circle indicates that the endpoint (5) is not included in the solution set.