1.
What is the coefficient in the expression 7p - 6
Correct Answer
B. 7
Explanation
The coefficient in the expression 7p - 6 is 7. The coefficient is the number that is multiplied by the variable, in this case, p. In the given expression, 7 is being multiplied by p, making it the coefficient.
2.
What are the variables in the expression 22b + 9b + c
Correct Answer
D. B and c
Explanation
The variables in the expression 22b + 9b + c are b and c. This is because both b and c are included in the expression and are being multiplied by coefficients (22 and 9) respectively. The terms "22b" and "9b" indicate that the variable b is being multiplied by the coefficients 22 and 9, while the term "c" indicates that the variable c is present in the expression.
3.
If 3x - 2 = 19, what is the value of x?
Correct Answer
A. 7
Explanation
The given equation is 3x - 2 = 19. To find the value of x, we need to isolate x on one side of the equation. Adding 2 to both sides, we get 3x = 21. Dividing both sides by 3, we find x = 7. Therefore, the correct answer is 7.
4.
Simplify: 18.4f + 11.2x - 1.2f
Correct Answer
B. 17.2f + 11.2x
Explanation
The given expression is a combination of terms with variables f and x. To simplify the expression, we can combine like terms by adding or subtracting coefficients that have the same variables. In this case, we have 18.4f and -1.2f, which can be combined to give us a total of 17.2f. The term 11.2x does not have any other term with the same variable, so it remains as it is. Therefore, the simplified expression is 17.2f + 11.2x.
5.
Simplify: 9.8c - 3.9c + 3.2b
Correct Answer
C. 5.9c + 3.2b
Explanation
The given expression is 9.8c - 3.9c + 3.2b. To simplify this expression, we combine the like terms. The like terms are the ones that have the same variable and exponent. In this case, we have 9.8c and -3.9c, which are like terms because they both have the variable c. When we subtract -3.9c from 9.8c, we get 5.9c. The other term in the expression is 3.2b, which remains the same. Therefore, the simplified expression is 5.9c + 3.2b.
6.
Simplify: 10x - 7x
Correct Answer
D. 3x
Explanation
The given expression is 10x - 7x. To simplify this, we subtract the coefficients of x, which are 10 and 7. 10x - 7x simplifies to 3x.
7.
Simplify: 12p + p
Correct Answer
A. 13p
Explanation
The expression 12p + p can be simplified by combining like terms. Since both terms have the variable p, they can be added together to get 13p.
8.
Simplify the expression: 9x - 4x
Correct Answer
D. 5x
Explanation
The expression 9x - 4x simplifies to 5x. This is because when subtracting like terms (terms with the same variable), we subtract the coefficients and keep the variable the same. In this case, 9x - 4x can be rewritten as 5x, where the coefficient 5 is the result of subtracting 4 from 9.
9.
Simplify the expression: 30x + 2 - 15x - 6 + 4
Correct Answer
B. 15x
Explanation
The expression can be simplified by combining like terms. The like terms in the expression are 30x and -15x, which can be combined to give 15x. The other terms, 2, -6, and 4, do not have any variables and can be combined to give 0. Therefore, the simplified expression is 15x + 0, which is equal to 15x.
10.
Simplify: -22 + 3x - 4y + 6z + x - 3y
Correct Answer
C. 4x + 6z - 7y - 22
Explanation
The given expression is simplified by combining like terms. The terms with the same variables are combined by adding or subtracting their coefficients. In this case, the like terms are 3x and x, which combine to give 4x. The terms -4y and -3y combine to give -7y. The term -22 does not have any like terms, so it remains as it is. The term 6z does not have any like terms either, so it also remains as it is. Thus, the simplified expression is 4z + 4x - 7y.
11.
Simplify: 4a + 5c - 6a
Correct Answer
A. 5c - 2a
Explanation
To simplify the given expression, we combine like terms by adding or subtracting coefficients of the same variables. In this case, we have 4a and -6a, which can be simplified to -2a. Similarly, we have 5c, which remains unchanged. Therefore, the simplified expression is 5c - 2a.
12.
Simplify the expression: 2x + 4 + 3 + 5x
Correct Answer
C. 7x + 7
Explanation
The given expression is 2x + 4 + 3 + 5x. To simplify it, we can combine like terms. The like terms in this expression are the terms with the variable x. Adding the coefficients of these terms, we get 2x + 5x = 7x. The constant terms in the expression are 4 and 3. Adding them, we get 4 + 3 = 7. Therefore, the simplified expression is 7x + 7.
13.
Simplify: 9y - 3y + 2y
Correct Answer
A. 8y
Explanation
The given expression is 9y - 3y + 2y. To simplify this expression, we combine the like terms. The terms with y can be added together, so we have 9y - 3y + 2y = (9 - 3 + 2)y = 8y. Therefore, the correct answer is 8y.
14.
Simplify: -6x + 8x
Correct Answer
D. 2x
Explanation
The given expression is -6x + 8x. To simplify this expression, we combine the like terms, which means adding the coefficients of x. -6x + 8x simplifies to 2x. Therefore, the correct answer is 2x.
15.
Simplify the expression: 8x - 4p + 1.2x
Correct Answer
C. 9.2x - 4p
Explanation
The given expression is 8x - 4p + 1.2x. To simplify this expression, we combine like terms by adding the coefficients of x and p. The coefficients of x are 8 and 1.2, so they can be added together to give 9.2x. The coefficient of p is -4, so it remains the same. Therefore, the simplified expression is 9.2x - 4p.