Simplify. -6 (1/4 x - 2/3 x + 5/6 x )
A: -x
B: -2 1/2 x
C: 3/4 x
D: 2x
To simplify the expression, we can combine the terms with the same variable (x).
-6 (1/4 x - 2/3 x + 5/6 x)
First, let's find a common denominator for the fractions. The least common multiple of 4, 3, and 6 is 12.
-6 (3/12 x - 8/12 x + 10/12 x)
Now, we can combine the fractions:
-6 (-5/12 x)
Multiplying -6 by -5/12:
= 30/12 x
Simplifying the fraction:
= 5/2 x
So, the simplified expression is 5/2 x. This is equivalent to 2 1/2 x.
Therefore, the answer is B: -2 1/2 x.
To simplify the expression -6 (1/4 x - 2/3 x + 5/6 x), follow these steps:
Step 1: Distribute -6 to each term inside the parentheses:
-6 (1/4 x) - 6 (-2/3 x) - 6 (5/6 x)
Step 2: Simplify each term:
-6/4 x + 12/3 x - 30/6 x
Step 3: Simplify the coefficients:
-3/2 x + 4x - 5x
Step 4: Combine like terms:
4x - 5x - 3/2 x
Step 5: Simplify the coefficients:
-1/2 x
Therefore, the simplified expression is -1/2 x.
To simplify the given expression, -6(1/4x - 2/3x + 5/6x), we can start by distributing the -6 to each term inside the parentheses.
-6(1/4x) = -6/4x = -3/2x
-6(-2/3x) = 12/3x = 4x
-6(5/6x) = -30/6x = -5x
Combining these results, we get:
-3/2x + 4x - 5x
Next, we can group the terms with the same variable together:
(-3/2x + 4x - 5x) = (-3/2x + 4x - 5x)
Now, we can combine the terms:
-3/2x + 4x - 5x = (-3/2 - 1 - 5)x = -9/2x
Therefore, the simplified expression is -9/2x.
Out of the given options, there is not an exact match for our simplified expression. However, we can see that option D: 2x is a multiple of our simplified expression -9/2x. To confirm, we can rearrange option D to see if it matches our simplified expression:
2x = 4/2x = 2/1x = 2x
Since 2x is not equal to -9/2x, option D is not correct. None of the given options exactly match our simplified expression -9/2x.