Which expression is equivalent to 1/4
x − 36?
Responses
A 1/4 (x + 144)
B 1/4 (x − 144)
C 1/4 (x − 9)
D 4x − 9
To find an expression equivalent to 1/4x - 36, you need to distribute the 1/4 to both terms in the parentheses.
The correct expression would be 1/4(x) - 1/4(36).
Simplifying further gives you 1/4x - 9.
Therefore, the correct expression is D) 4x - 9.
wrong
Apologies for the incorrect response.
Let's distribute 1/4 to both terms in the expression 1/4x - 36:
1/4 * x = x/4
1/4 * -36 = -36/4 = -9
So, the equivalent expression is x/4 - 9, which can be simplified as 1/4 (x - 36).
Therefore, the correct expression is C) 1/4 (x - 36).
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 an equivalent expression to -1/5(10x + 15) - 2, you need to distribute the -1/5 to both terms in the parentheses and then combine like terms.
First, distribute -1/5 to 10x and 15:
-1/5 * 10x = -10/5 * x = -2x
-1/5 * 15 = -15/5 = -3
So, the expression becomes -2x - 3.
Therefore, the correct expression is C) -2x - 3.
To find an expression equivalent to 1/4(x - 36), we can distribute the 1/4 to both terms inside the parentheses.
1/4(x - 36) = 1/4 * x - 1/4 * 36
Simplifying this expression gives us:
1/4(x - 36) = 1/4x - 9
Therefore, the correct expression equivalent to 1/4(x - 36) is 1/4x - 9, which corresponds to option D.
To simplify the expression 1/4x - 36, you need to distribute the 1/4 to both terms inside the parentheses.
So, 1/4 multiplied by x gives you 1/4x, and 1/4 multiplied by -36 gives you -9.
Therefore, the equivalent expression is 1/4x - 36 = 1/4(x) + (-9).
Looking at the options:
A. 1/4 (x + 144) - This does not match the equivalent expression because the sign of the second term is incorrect.
B. 1/4 (x - 144) - This does not match the equivalent expression because the sign of the second term is incorrect.
C. 1/4 (x - 9) - This matches the equivalent expression, as it correctly distributes the 1/4 and has the same sign as the second term.
D. 4x - 9 - This expression is not equivalent to the given expression.
Therefore, the correct answer is C. 1/4 (x - 9).