Simplify 3 - (4x - 5) + 6.
Responses
A 12x + 2112x + 21
B 4x + 144x + 14
C 4x + 44x + 4
D -4x + 14-4x + 14
E -4x + 4
To simplify 3 - (4x - 5) + 6, distribute the negative sign to the terms inside the parentheses:
3 - 4x + 5 + 6
Combine like terms:
(3 + 5 + 6) - 4x
14 - 4x
Therefore, the simplified expression is: 14 - 4x.
Simplify 3 - (4x - 5) + 6.
Responses
A 12x + 21
B 4x + 14
C 4x + 4
D -4x + 14
E -4x + 4
To simplify 3 - (4x - 5) + 6, distribute the negative sign to the terms inside the parentheses:
3 - 4x + 5 + 6
Combine like terms:
14 - 4x
So the simplified expression is 14 - 4x.
Therefore, the correct response is:
D) -4x + 14
Use the distributive property to expand the linear expression.
3(4x + 3)
A.3/4
B.12x+6
C.12x + 9
D.-3/4
To expand the linear expression 3(4x + 3), distribute the 3 to each term inside the parentheses:
3 * 4x + 3 * 3
This simplifies to:
12x + 9
Therefore, the correct response is:
C) 12x + 9
Which two statements are correct when simplifying this expression?
12 + 6(3x − 2)
To simplify the expression 12 + 6(3x - 2), you need to distribute the 6 to each term inside the parentheses:
12 + 6 * 3x - 6 * 2
Which simplifies to:
12 + 18x - 12
Now, combine like terms:
(12 - 12) + 18x
The simplified expression becomes:
0 + 18x
Since anything multiplied by 0 is 0, the final simplified expression is:
18x
Therefore, the two correct statements when simplifying the expression 12 + 6(3x - 2) are:
1) The constant terms subtracted each other (12 - 12), resulting in zero.
2) The simplified expression is 18x.
Which expression is equivalent to -4(y – 7)?
Responses
A -4y - 28-4 y - 28
B -4y - 7-4 y - 7
C -4y - 11-4 y - 11
D -4y + 28
To find the expression equivalent to -4(y - 7), you need to distribute the -4 to each term inside the parentheses:
-4 * y - 4 * (-7)
Which simplifies to:
-4y + 28
Therefore, the correct response 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), you need to distribute the 2/3 to each term inside the parentheses:
2/3 * 4x - 2/3 * 9
Which simplifies to:
8/3x - 18/3
Simplifying further, you can simplify the fractions:
8/3x - 6
Therefore, the correct response is:
B) 8x - 6
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 77
B yy
C zz
D xx
E 6
To factor the expression 42xyz + 56xy - 7x, Steven needs to find a common factor among all the terms.
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42.
The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, and 56.
The factors of 7 are: 1 and 7.
The factors of x are: x.
The factors of y are: y.
The factors of z are: z.
Based on these factors, Steven could use the common factors:
A) 77 (7 is a factor of all terms).
E) 6 (2 is a factor of the first term and 7 is a factor of the last two terms).
Therefore, the correct responses are:
A) 77
E) 6
Which expression is equivalent to 2(2x + 7)?
To find the expression equivalent to 2(2x + 7), you need to distribute the 2 to each term inside the parentheses:
2 * 2x + 2 * 7
Which simplifies to:
4x + 14
Therefore, the expression equivalent to 2(2x + 7) is:
4x + 14