Which expression is equivalent to -4(y – 7)?
Responses are
1. -4y - 28
2. -4y - 7
3. -4y - 11
4. 4y + 28
The expression -4(y – 7) can be simplified by distributing the -4 to both terms inside the parentheses. This gives us -4y + 28.
Therefore, the equivalent expression is -4y + 28.
Option 4, 4y + 28, is incorrect because the sign of -4 is negative and not positive.
Which two statements are correct when simplifying this expression?
12 + 6(3x − 2)
1. First, calculate 6(3x − 2)
2. First, calculate 12 + 6.
3. 12 + 6(3x − 2) = 54x − 36
4. 12 + 6(3x − 2) = 18x
5.12 + 6(3x − 2) = 18x − 24
The correct statements when simplifying the expression 12 + 6(3x − 2) are:
1. First, calculate 6(3x − 2)
2. 12 + 6(3x − 2) = 18x − 12
Option 3, 12 + 6(3x − 2) = 54x − 36, is incorrect because the distributive property should be applied to both terms inside the parentheses, resulting in 18x − 12 and not 54x − 36.
Option 4, 12 + 6(3x − 2) = 18x, is incorrect because the term -12 from the distributive property is omitted.
Option 5, 12 + 6(3x − 2) = 18x − 24, is incorrect because the expression should be simplified to 18x − 12 and not 18x − 24.
Which expression is equivalent to 2(2x + 7)?
4x - 14
4x + 14
14x + 4
8x + 14
The expression 2(2x + 7) can be simplified by distributing the 2 to both terms inside the parentheses. This gives us 4x + 14.
Therefore, the equivalent expression is 4x + 14.
Option 1, 4x - 14, is incorrect because the sign of 14 is positive and not negative.
Option 2, 4x + 14, is the correct answer.
Option 3, 14x + 4, is incorrect because the coefficients are not multiplied together and the signs are different.
Option 4, 8x + 14, is incorrect because the coefficient of x is 4 and not 8.
Use the distributive property to expand the linear expression.
3(4x + 3)
1. 3/4
2. 12x + 6
3.12x + 9
4. -3/4
To expand the linear expression 3(4x + 3), we can distribute the 3 to both terms inside the parentheses.
This gives us 12x + 9.
Therefore, the correct answer is option 3, 12x + 9.
Options 1, 3/4, and 4 are incorrect because they do not represent the expanded expression.