Question
1. 8.1(3.14)
2. Evaluate 3t(t + 2) - 3t^2 for t = 19
3. 3(x + 1) = 9 + 2x
Solve each inequality. Graph the solution.
1. 2(5 - 3x) < x - 4(3 - x)
2. 10 > 7 + 3x and 9 - 4x < 1
3. 3 > 2x or x - 4 > 2
2. Evaluate 3t(t + 2) - 3t^2 for t = 19
3. 3(x + 1) = 9 + 2x
Solve each inequality. Graph the solution.
1. 2(5 - 3x) < x - 4(3 - x)
2. 10 > 7 + 3x and 9 - 4x < 1
3. 3 > 2x or x - 4 > 2
Answers
Answer
Name the subset(s) of real numbers to which each number belongs.
12 7/8
12 7/8
Answer
8.1(3.14)
Name the subset(s) of real numbers to which each number belongs.
Name the subset(s) of real numbers to which each number belongs.
Answer
Solve each equation. Check for extraneous solutions.
3|x + 10| = 6
Solve each inequality. Graph the solution.
4|y - 9|>36
1/2|x + 2| > 6
3|x + 10| = 6
Solve each inequality. Graph the solution.
4|y - 9|>36
1/2|x + 2| > 6
Answered by
GPT 3.5
1. 8.1(3.14) = 25.134
2. Evaluate 3t(t + 2) - 3t^2 for t = 19:
3(19)(19 + 2) - 3(19^2)
= 3(19)(21) - 3(361)
= 1197 - 1083
= 114
3. 3(x + 1) = 9 + 2x:
3x + 3 = 9 + 2x
x + 3 = 9
x = 6
Solving inequalities:
1. 2(5 - 3x) < x - 4(3 - x):
10 - 6x < x - 12 + 4x
-5x < -2x - 2
-3x < -2
x > 2/3
2. 10 > 7 + 3x and 9 - 4x < 1:
3x < 3
x < 1
9 - 4x < 1
-4x < -8
x > 2
Solutions: x < 1 and x > 2
3. 3 > 2x or x - 4 > 2:
2x < 3
x < 3/2
x - 4 > 2
x > 6
Solution: x < 3/2 or x > 6
2. Evaluate 3t(t + 2) - 3t^2 for t = 19:
3(19)(19 + 2) - 3(19^2)
= 3(19)(21) - 3(361)
= 1197 - 1083
= 114
3. 3(x + 1) = 9 + 2x:
3x + 3 = 9 + 2x
x + 3 = 9
x = 6
Solving inequalities:
1. 2(5 - 3x) < x - 4(3 - x):
10 - 6x < x - 12 + 4x
-5x < -2x - 2
-3x < -2
x > 2/3
2. 10 > 7 + 3x and 9 - 4x < 1:
3x < 3
x < 1
9 - 4x < 1
-4x < -8
x > 2
Solutions: x < 1 and x > 2
3. 3 > 2x or x - 4 > 2:
2x < 3
x < 3/2
x - 4 > 2
x > 6
Solution: x < 3/2 or x > 6
Answered by
GPT 3.5
12 belongs to the subset of real numbers called integers.
7/8 belongs to the subset of real numbers called rational numbers.
7/8 belongs to the subset of real numbers called rational numbers.
Answered by
GPT 3.5
8.1(3.14) is a multiplication of two numbers, 8.1 and 3.14.
Both 8.1 and 3.14 belong to the subset of real numbers called irrational numbers, as they cannot be expressed as a fraction and have an infinite number of decimal places.
Both 8.1 and 3.14 belong to the subset of real numbers called irrational numbers, as they cannot be expressed as a fraction and have an infinite number of decimal places.
Answered by
GPT 3.5
To solve the equation 3|x + 10| = 6, we can split it into two cases based on the absolute value expression:
Case 1: x + 10 is non-negative (x + 10 ≥ 0)
In this case, the equation becomes 3(x + 10) = 6:
3x + 30 = 6
3x = -24
x = -8
However, we need to check if x = -8 satisfies the absolute value inequality. Plugging it back into the equation:
3|-8 + 10| = 6
3|2| = 6
6 = 6
Since -8 satisfies the equation, it is a valid solution.
Case 2: x + 10 is negative (x + 10 < 0)
In this case, the equation becomes 3(-x - 10) = 6 (we multiply by -1 to remove the negative sign):
-3x - 30 = 6
-3x = 36
x = -12
Checking if x = -12 satisfies the absolute value inequality:
3|-12 + 10| = 6
3|-2| = 6
6 = 6
Thus, the solution to the equation 3|x + 10| = 6 is x = -8 and x = -12.
To solve the inequality 4|y - 9| > 36, we can similarly split it into two cases based on the absolute value expression:
Case 1: y - 9 is non-negative (y - 9 ≥ 0)
In this case, the inequality becomes 4(y - 9) > 36:
4y - 36 > 36
4y > 72
y > 18
Case 2: y - 9 is negative (y - 9 < 0)
In this case, the inequality becomes 4(-y + 9) > 36:
-4y + 36 > 36
-4y > 0
y < 0
Thus, the solution to the inequality 4|y - 9| > 36 is y < 0 or y > 18.
To solve the inequality 1/2|x + 2| > 6, we can again split it into two cases based on the absolute value expression:
Case 1: x + 2 is non-negative (x + 2 ≥ 0)
In this case, the inequality becomes 1/2(x + 2) > 6:
1/2x + 1 > 6
1/2x > 5
x > 10
Case 2: x + 2 is negative (x + 2 < 0)
In this case, the inequality becomes 1/2(-x - 2) > 6:
-1/2x - 1 > 6
-1/2x > 7
x < -14
Thus, the solution to the inequality 1/2|x + 2| > 6 is x < -14 or x > 10.
Case 1: x + 10 is non-negative (x + 10 ≥ 0)
In this case, the equation becomes 3(x + 10) = 6:
3x + 30 = 6
3x = -24
x = -8
However, we need to check if x = -8 satisfies the absolute value inequality. Plugging it back into the equation:
3|-8 + 10| = 6
3|2| = 6
6 = 6
Since -8 satisfies the equation, it is a valid solution.
Case 2: x + 10 is negative (x + 10 < 0)
In this case, the equation becomes 3(-x - 10) = 6 (we multiply by -1 to remove the negative sign):
-3x - 30 = 6
-3x = 36
x = -12
Checking if x = -12 satisfies the absolute value inequality:
3|-12 + 10| = 6
3|-2| = 6
6 = 6
Thus, the solution to the equation 3|x + 10| = 6 is x = -8 and x = -12.
To solve the inequality 4|y - 9| > 36, we can similarly split it into two cases based on the absolute value expression:
Case 1: y - 9 is non-negative (y - 9 ≥ 0)
In this case, the inequality becomes 4(y - 9) > 36:
4y - 36 > 36
4y > 72
y > 18
Case 2: y - 9 is negative (y - 9 < 0)
In this case, the inequality becomes 4(-y + 9) > 36:
-4y + 36 > 36
-4y > 0
y < 0
Thus, the solution to the inequality 4|y - 9| > 36 is y < 0 or y > 18.
To solve the inequality 1/2|x + 2| > 6, we can again split it into two cases based on the absolute value expression:
Case 1: x + 2 is non-negative (x + 2 ≥ 0)
In this case, the inequality becomes 1/2(x + 2) > 6:
1/2x + 1 > 6
1/2x > 5
x > 10
Case 2: x + 2 is negative (x + 2 < 0)
In this case, the inequality becomes 1/2(-x - 2) > 6:
-1/2x - 1 > 6
-1/2x > 7
x < -14
Thus, the solution to the inequality 1/2|x + 2| > 6 is x < -14 or x > 10.
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