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Explanation To find the value of x, we need to isolate it on one side of the equation. First, we subtract 10 from both sides of the equation: 5x = -35. Then, we divide both sides by 5 to solve for x: x = -7. Therefore, the answer is -7.
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2.
7 + 5x = 14 + 6x
A.
-7
B.
7
C.
10
D.
-10
Correct Answer A. -7
Explanation To solve the equation 7 + 5x = 14 + 6x, we want to isolate the variable x on one side of the equation. We can do this by subtracting 6x from both sides of the equation to get 7 + 5x - 6x = 14. Simplifying this gives us 7 - x = 14. To isolate x, we need to get rid of the constant term 7. We can do this by subtracting 7 from both sides of the equation, resulting in -x = 7. Finally, we multiply both sides of the equation by -1 to solve for x, giving us x = -7.
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3.
2x - 10 = 3(2 - 2x)
A.
8
B.
6
C.
4
D.
2
Correct Answer D. 2
Explanation The equation 2x - 10 = 3(2 - 2x) can be solved by simplifying both sides of the equation. Distributing the 3 on the right side gives 6 - 6x. Combining like terms on the left side gives 2x + 10. Setting the two sides equal to each other, we get 2x + 10 = 6 - 6x. Adding 6x to both sides gives 8x + 10 = 6. Subtracting 10 from both sides gives 8x = -4. Dividing both sides by 8 gives x = -0.5. Therefore, the correct answer is 2.
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4.
2(x + 4) - 2 = -12
A.
-3
B.
3
C.
9
D.
-9
Correct Answer D. -9
Explanation The given equation is 2(x + 4) - 2 = -12. To solve this equation, we first simplify the expression inside the parentheses by multiplying 2 with both x and 4. This gives us 2x + 8. The equation now becomes 2x + 8 - 2 = -12. We combine like terms by subtracting 2 from 8, which gives us 2x + 6 = -12. To isolate the variable, we subtract 6 from both sides of the equation, resulting in 2x = -18. Finally, we divide both sides by 2 to solve for x, giving us x = -9. Therefore, the correct answer is -9.
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5.
2x + 6 - 8x - 8 = 10
A.
3
B.
-3
C.
-2
D.
2
Correct Answer C. -2
Explanation The given equation is a linear equation in one variable. To solve it, we need to combine like terms and isolate the variable on one side of the equation. By adding 8x to both sides and simplifying, we get -6x + 6 = 10. Then, by subtracting 6 from both sides, we obtain -6x = 4. Finally, we divide both sides by -6 to solve for x, which gives us x = -2. Therefore, the correct answer is -2.
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6.
X + 6 = 4x
A.
1
B.
2
C.
3
D.
4
Correct Answer B. 2
Explanation The correct answer is 2. To solve the equation x + 6 = 4x, we need to isolate the variable x. We can do this by subtracting x from both sides of the equation, which gives us 6 = 3x. Then, we divide both sides by 3 to solve for x, resulting in x = 2.
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7.
3x + 5 = 10 - 2x
A.
-1
B.
0
C.
1
D.
2
Correct Answer C. 1
Explanation To solve the equation 3x + 5 = 10 - 2x, we need to isolate the variable x. First, we can combine like terms by adding 2x to both sides of the equation, resulting in 5x + 5 = 10. Then, we can subtract 5 from both sides to get 5x = 5. Finally, we can divide both sides by 5 to solve for x, giving us x = 1.
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8.
11x - 3x = 2(x - 3)
A.
-1
B.
0
C.
1
D.
2
Correct Answer A. -1
Explanation The given equation is 11x - 3x = 2(x - 3). To solve this equation, we can simplify both sides by combining like terms. On the left side, 11x - 3x simplifies to 8x. On the right side, 2(x - 3) can be expanded to 2x - 6. Therefore, the equation becomes 8x = 2x - 6. To isolate the variable, we can subtract 2x from both sides, resulting in 6x = -6. Finally, dividing both sides by 6 gives us x = -1. Therefore, the correct answer is -1.
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9.
10 = 2x + 6 - 8x - 14
A.
-2
B.
2
C.
3
D.
-3
Correct Answer D. -3
Explanation The equation given is 10 = 2x + 6 - 8x - 14. To solve for x, we can combine like terms: 10 = -6x - 8. By adding 6x to both sides, we get 6x + 10 = -8. Then, by subtracting 10 from both sides, we have 6x = -18. Finally, dividing both sides by 6 gives us x = -3.
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10.
-3(4x + 3) + 4(6x + 1) = 43
A.
3
B.
4
C.
-4
D.
10
Correct Answer B. 4
Explanation To solve the given equation, we need to distribute the coefficients and simplify. Distributing -3 to (4x + 3) gives -12x - 9, and distributing 4 to (6x + 1) gives 24x + 4. Combining like terms, we have -12x - 9 + 24x + 4 = 43. Simplifying further, we get 12x - 5 = 43. Adding 5 to both sides gives 12x = 48, and dividing by 12 gives x = 4. Therefore, the correct answer is 4.
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11.
BONUS: The sum of 2 consecutive odd integers is 36. What is the largest integer?
Correct Answer 19
Explanation The sum of two consecutive odd integers is 36. Since the integers are consecutive, we can represent them as x and x+2. Setting up an equation, we have x + (x+2) = 36. Combining like terms, we get 2x + 2 = 36. Solving for x, we subtract 2 from both sides to get 2x = 34. Dividing both sides by 2, we find x = 17. Therefore, the largest integer is 17+2 = 19.
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