1.
1. Simplify: 4x + 3y - 6 + 2
Correct Answer
D. 4x + 3y - 4
Explanation
The given expression is 4x + 3y - 6 + 2. We can simplify this expression by combining like terms. The like terms in this expression are 4x and -6. When we combine these terms, we get 4x - 6. The expression also includes 3y and 2, which are unlike terms and cannot be combined. Therefore, the simplified expression is 4x + 3y - 6 + 2 = 4x + 3y - 4.
2.
2. Simplify: 3a + 2b + a - 3b + 5
Correct Answer
A. 4a - b + 5
Explanation
The given expression involves combining like terms. We can combine the terms 3a and a to get 4a. Similarly, we can combine the terms 2b and -3b to get -b. Finally, we can combine the constant terms 5 and 0 to get 5. Therefore, the simplified expression is 4a - b + 5.
3.
3. Simplify: 9x + 9y - 4x + 3x - 2y - 8
Correct Answer
C. 8x + 7y - 8
Explanation
The given expression is a combination of like terms. To simplify it, we can combine the coefficients of the like terms. In this case, the like terms are the terms with x and y. Combining the coefficients of x, we have 9x - 4x + 3x = 8x. Combining the coefficients of y, we have 9y - 2y = 7y. The constant term -8 remains the same. Therefore, the simplified expression is 8x + 7y - 8.
4.
4. Simplify: 3(2x - 4) + 2 - 4x
Correct Answer
B. 2x - 10
Explanation
The given expression is 3(2x - 4) + 2 - 4x. To simplify this expression, we can distribute the 3 to the terms inside the parentheses: 6x - 12 + 2 - 4x. Combining like terms, we have 6x - 4x - 12 + 2. Simplifying further, we get 2x - 10.
5.
5. Solve: 3(x + 5) + 4 = 31
Correct Answer
B. X = 4
Explanation
To solve the equation, we first distribute the 3 to both terms inside the parentheses: 3x + 15 + 4 = 31. Then, we combine like terms by adding 15 and 4: 3x + 19 = 31. Next, we isolate the variable by subtracting 19 from both sides: 3x = 12. Finally, we solve for x by dividing both sides by 3: x = 4.
6.
6. Simplify: 6(x + 3) - 4x + 2
Correct Answer
C. 2x + 20
Explanation
To simplify the given expression, we apply the distributive property by multiplying 6 with both terms inside the parentheses: 6(x + 3) = 6x + 18. Then, we combine like terms by subtracting 4x from 6x to get 2x. Finally, we add 18 and 2 to get 20. Therefore, the simplified expression is 2x + 20.
7.
7. Solve: 4x - 8 + 3x = 34
Correct Answer
B. X = 6
Explanation
The equation given is a linear equation in one variable. To solve it, we can combine like terms by adding the coefficients of x, which gives us 7x - 8 = 34. Next, we can isolate the variable by adding 8 to both sides, resulting in 7x = 42. Finally, we can solve for x by dividing both sides of the equation by 7, giving us x = 6.
8.
8. Solve:
Correct Answer
B. Y = 4
Explanation
The correct answer is y = 4 because it is the only equation that satisfies the given conditions. The other equations, y = 2, y = 1/2, and y = 1/4, do not match the given values. Therefore, y = 4 is the only solution that fits the given equations.