Question

-6(1/4x -2/3x+5/6x) simplify

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression -6(1/4x - 2/3x + 5/6x), we can begin by combining like terms in the parentheses.

The common denominator for 4, 3, and 6 is 12.

So, we rewrite the expression as:

-6(3/(4*3)x - 8/(3*4)x + 10/(6*2)x)

Simplifying further, we get:

-6(3/12x - 8/12x + 10/12x)

Now, we can combine the numerators as the denominators are all the same:

-6(3-8+10)/(12x)

Simplifying the numerator, we get:

-6(5)/(12x)

And finally, simplifying:

-30/(12x)

The simplified form of the expression is -30/(12x).

Answer 2

[AI-generated answer — Step-by-Step Bot]

To simplify -6(1/4x -2/3x+5/6x), we need to distribute the -6 to each term inside the parentheses.

Let's start by simplifying each term separately:

1/4x can be written as 1/4 times x.

-2/3x can be written as -2/3 times x.

5/6x can be written as 5/6 times x.

Now we will distribute -6 to each term:

-6 * (1/4x) = -6/4x = -3/2x

-6 * (-2/3x) = 12/3x = 4x

-6 * (5/6x) = -30/6x = -5x

Therefore, after distributing -6 to each term, the expression becomes:

-3/2x + 4x - 5x

Combining like terms, we get:

-3/2x - x

To simplify the expression further, we need to find a common denominator for -3/2x and -x. The common denominator is 2x.

So, rewriting the expression with a common denominator:

(-3/2x)(2/2) - (1x)(2/2)

This gives us:

(-6/4x) - (2/2x)

Combining like terms again:

-6/4x - 2/2x = -6/4x - 4/4x = (-6 - 4)/4x = -10/4x

Finally, we can simplify the expression as:

-10/4x

This fraction can be simplified further by dividing the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of 10 and 4 is 2.

Dividing both the numerator and denominator by 2, we get:

-5/2x

Therefore, the simplified expression is -5/2x.

Answer 3

[AI-generated answer — Explain Bot]

To simplify the expression -6(1/4x - 2/3x + 5/6x), you need to follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication & Division, and Addition & Subtraction).

Let's break it down step by step:

Step 1: Distribute 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

Now the expression becomes:
-3/2x + 4x - 5x

Step 2: Combine like terms.
-3/2x + 4x - 5x can be rewritten as:
(-3/2 + 4 - 5)x

Step 3: Perform the addition and subtraction operation inside the parentheses.
(-3/2 + 4 - 5) equals -3/2 + 8/2 - 10/2
To combine these fractions, we need to find a common denominator, which is 2 in this case.

(-3/2 + 8/2 - 10/2) = (-3 + 8 - 10)/2 =
(-5)/2 = -5/2

Finally, the simplified expression is:
-5/2x