Use the distributive property to expand the linear expression.
3(4x + 3)
Responses
A 3/4
B 12x + 6
C 12x + 9
D -3/4
To expand the linear expression using the distributive property, we need to multiply each term inside the parentheses by the coefficient outside the parentheses.
Using the distributive property:
3(4x + 3) = 3 * 4x + 3 * 3
Simplifying:
12x + 9
Thus, the expanded form of the linear expression is 12x + 9.
The correct option is C) 12x + 9.
Which expression is equivalent to 2(2x + 7)?
Responses
A 4x - 14
B 4x + 14
C 14x + 4
D 8x + 14
To find the expression equivalent to 2(2x + 7), we need to apply the distributive property.
Multiplying each term inside the parentheses by the coefficient outside the parentheses:
2(2x + 7) = 2 * 2x + 2 * 7
Simplifying:
4x + 14
Thus, the expression equivalent to 2(2x + 7) is 4x + 14.
The correct option is B) 4x + 14.
Which expression is equivalent to -4(y – 7)?
Responses
A -4y - 28
B -4y - 7
C -4y - 11
D -4y + 28
To find the expression equivalent to -4(y - 7), we need to apply the distributive property.
Multiplying each term inside the parentheses by the coefficient outside the parentheses:
-4(y - 7) = -4 * y + -4 * (-7)
Simplifying:
-4y + 28
Thus, the expression equivalent to -4(y - 7) is -4y + 28.
The correct option is D) -4y + 28.
Which expression in equivalent to 2/3(4x - 9)?
Responses
A 8x - 18/3
B 8x - 9/3
C 8/3(x + 18)
D 8/3(x - 12)
To find the expression equivalent to 2/3(4x - 9), we need to apply the distributive property.
Multiplying each term inside the parentheses by the coefficient outside the parentheses:
2/3(4x - 9) = 2/3 * 4x - 2/3 * 9
Simplifying:
8x/3 - 18/3
The fractions 8x/3 and 18/3 can be simplified further:
8x/3 - 18/3 = (8x - 18)/3
Thus, the expression equivalent to 2/3(4x - 9) is (8x - 18)/3.
The correct option is A) 8x - 18/3. (However, this answer can be simplified to 8x - 6)
Which two statements are correct when simplifying this expression?
12 + 6(3x − 2)
Responses
A First, calculate 6(3x − 2)
B First, calculate 12 + 6.
C 12 + 6(3x − 2) = 54x - 36
D 12 + 6(3x − 2) = 18x
E 12 + 6(3x − 2) = 18x − 24
The correct statements when simplifying the expression 12 + 6(3x - 2) are:
A) First, calculate 6(3x - 2): This is correct because we need to simplify the expression inside the parentheses first before performing any other operations.
D) 12 + 6(3x - 2) = 18x: This is also correct because once we simplify the expression inside the parentheses, we are left with 18x. Adding 12 to this expression does not change the term with x.
The correct statements are A) First, calculate 6(3x - 2) and D) 12 + 6(3x - 2) = 18x.
Which expression is equivalent to 1/4x − 36?
Responses
A 1/4 (x + 144)
B 1/4(x − 144)
C 1/4(x − 9)
D 4x − 9