Question

Subtract 1/2(z+4)−3(1/4z+1) . Use fractions in final form.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify this expression, we need to distribute and combine like terms. Let's start by distributing the 1/2 to (z + 4) and the -3 to (1/4z + 1):

1/2 * (z + 4) - 3 * (1/4z + 1)

= (1/2 * z) + (1/2 * 4) - (3 * 1/4 * z) - (3 * 1)

= (1/2z) + 2/2 - (3/4z) - 3

Now, let's combine the like terms:

= 1/2z + 2/2 - 3/4z - 3

= 1/2z - 3/4z + 2/2 - 3

To add or subtract fractions, we need a common denominator. In this case, the least common denominator (LCD) is 4. Let's rewrite the fractions with the common denominator:

= 2/4z - 3/4z + 2/2 - 3

Now, let's combine the like terms:

= (2 - 3)/4z + 2/2 - 3

= (-1)/4z + 1 - 3

= -1/4z - 2

Therefore, the final simplified form of 1/2(z + 4) - 3(1/4z + 1) is -1/4z - 2.

Answer 2

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

To subtract the expression 1/2(z+4) - 3(1/4z+1), we need to distribute the coefficients of z and the constants inside the parentheses.

Let's start by distributing 1/2 into (z+4):

(1/2) * (z+4) = (1/2) * z + (1/2) * 4 = z/2 + 2

Next, let's distribute -3 into (1/4z+1):

-3 * (1/4z+1) = -3 * (1/4z) + (-3) * 1 = -3/4z - 3

Now we can rewrite the expression using the distributed terms:

1/2(z+4) - 3(1/4z+1) = z/2 + 2 - 3/4z - 3

Now, let's combine the like terms:

z/2 - 3/4z + 2 - 3 = (4z - 3z)/8 - 9/8 + 16/8 = z/8 - 9/8 + 16/8

Finally, we can combine the fractions:

z/8 - 9/8 + 16/8 = (z - 9 + 16) / 8 = (z + 7) / 8

So the final answer, using fractions in simplest form, is (z + 7) / 8.

Answer 3

[AI-generated answer — Explain Bot]

To subtract the given expression, we need to simplify each term individually and then combine like terms.

First, let's simplify the terms:

1/2(z+4) = (1/2)(z) + (1/2)(4) = (1/2)z + 2

3(1/4z+1) = (3)(1/4z) + (3)(1) = (3/4)z + 3

Now we can subtract the two simplified terms:

(1/2)z + 2 - ((3/4)z + 3)

To subtract the terms, we need to distribute the negative sign to both terms within the parentheses:

(1/2)z + 2 - (3/4)z - 3

Now we can combine like terms:

(1/2)z - (3/4)z + 2 - 3

To combine the z terms, we need to find a common denominator for 2 and 4, which is 4. Therefore, we can rewrite the expression as:

(2/4)z - (3/4)z + 2 - 3

Next, we can combine the like terms:

(-1/4)z - 1

So, the final simplified form of the expression is (-1/4)z - 1.