Which expression is equivalent to 1/4x − 36?
A 1/4 (x + 144)
B 1/4(x − 144)
C 1/4(x − 9)
D 4x − 9
The correct expression that is equivalent to 1/4x − 36 is A) 1/4 (x + 144).
Which expression is equivalent to -
-1/5(10x + 1/5) - 2?
Responses
A -2x – 1
B -2x – 4
C -2x – 3
D -2x – 5
To simplify the expression -1/5(10x + 1/5) - 2, we can start by distributing the -1/5 to both terms inside the parentheses:
-1/5(10x) - 1/5(-1/5) - 2
This simplifies to:
-2x - 1/25 - 2
Next, we can simplify -1/25 - 2 by finding a common denominator:
-2x - (1/25)(25/25) - (2)(25/25)
This simplifies to:
-2x - 25/25 - 50/25
The fraction -25/25 is equal to -1, and -50/25 is equal to -2, so the expression simplifies further to:
-2x - 1 - 2
Finally, we can combine like terms:
-2x - 3
Therefore, the expression -1/5(10x + 1/5) - 2 is equivalent to C) -2x - 3.
To find the equivalent expression to 1/4x - 36, we need to simplify the expression.
First, distribute the 1/4 to x and -36:
1/4 * x - 1/4 * 36
= 1/4x - 9
So, the expression is equivalent to 1/4x - 9.
Therefore, the correct option is D) 4x - 9.
To find the equivalent expression to 1/4x - 36, we need to simplify it further.
First, we can distribute 1/4 to the terms inside the parentheses:
1/4 * x - 1/4 * 36
This simplifies to:
x/4 - 9
Now, let's compare this with the options given:
A) 1/4(x + 144) - This is not equivalent, as it has a different number added to x.
B) 1/4(x - 144) - This is not equivalent, as it has a different number subtracted from x.
C) 1/4(x - 9) - This is equivalent! It has the same expression inside the parentheses, and the same subtraction of 9.
D) 4x - 9 - This is not equivalent, as the whole expression is multiplied by 4 instead of just x.
Therefore, the answer is C) 1/4(x - 9).