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
To find the expression equivalent to 1/4x - 36, we need to distribute the 1/4 to the term inside the parentheses.
1/4x - 36 = (1/4)x - 36 = (x/4) - 36
Thus, the expression equivalent to 1/4x - 36 is (x/4) - 36.
The correct option is C) 1/4(x - 9).
Steven will factor the expression 42xyz + 56xy – 7x by dividing each term by a common factor. Which possible common factor could Steven use? (choose 2)
Responses
A 7
B y
C z
D x
E 6
To factor the expression 42xyz + 56xy - 7x by dividing each term by a common factor, we need to find the greatest common factor (GCF) of the terms. The GCF is the largest number or variable that can divide evenly into each term.
From the given expression, the GCF would be a factor that divides evenly into each term: 42xyz, 56xy, and 7x.
The two possible common factors that Steven could use are:
A) 7
D) x
Both 7 and x can divide evenly into each term in the expression.
Therefore, the correct options are A) 7 and D) x.
Simplify 3 - (4x - 5) + 6.
Responses
A 12x + 21
B 4x + 14
C 4x + 4
D -4x + 14
E -4x + 4
To simplify the expression 3 - (4x - 5) + 6, we need to remove the parentheses and combine like terms.
Note that the negative sign in front of the parentheses means that we need to distribute the negative sign to each term inside the parentheses.
3 - (4x - 5) + 6 = 3 - 4x + 5 + 6
Next, we can combine the constants and then combine the terms with x:
= (3 + 5 + 6) - 4x
= 14 - 4x
Thus, the simplified expression is 14 - 4x.
The correct option is E) -4x + 14.
Which expression is equivalent to 2/3x + 1?
Responses
A 1/3(2x + 3)
B 2/3(2x + 3)
C 2/3 (3x + 2)
D 2/3(3x + 1)
To find the expression that is equivalent to 2/3x + 1, we can rearrange the terms and apply the distributive property.
2/3x + 1 = 1 + 2/3x
Now, we can see that the expression can be rewritten as:
1 + 2/3x = 2/3(3x) + 1
Simplifying further:
2/3(3x) + 1 = 2/3(3x) + 3/3 = 2x + 3/3
The fraction 3/3 simplifies to 1, so the expression can be further simplified to:
2x + 1
Thus, the equivalent expression is 2x + 1.
The correct option is not provided in the responses.
?
Apologies for the confusion. It seems that none of the provided options match the equivalent expression of 2/3x + 1. Please note that the equivalent expression is 2/3x + 1. None of the responses provided accurately represent the equivalent expression.
Which expression is equivalent to -
-1/5(10x + 15) - 2?
Responses
A -2x – 1
B -2x – 4
C -2x – 3
D -2x – 5
To find the expression that is equivalent to -1/5(10x + 15) - 2, we need to apply the distributive property and simplify.
-1/5(10x + 15) - 2 = (-1/5)(10x) + (-1/5)(15) - 2
Simplifying the terms inside parentheses:
= -2x - 3 - 2
Combining like terms:
= -2x - 5
Thus, the expression that is equivalent to -1/5(10x + 15) - 2 is -2x - 5.
The correct option is D) -2x - 5.