Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To subtract 1/2(z+4) - 3(1/4z+1), we need to first distribute the coefficients to each term inside the parentheses.

Starting with the first term, we distribute 1/2 to (z+4):

1/2 * z = z/2
1/2 * 4 = 4/2 = 2

So, the first term becomes: z/2 + 2

Now, let's distribute 3 to (1/4z+1):

3 * 1/4z = 3/4z
3 * 1 = 3

So, the second term becomes: 3/4z + 3

Now we can simplify the expression:

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

Notice that we have a common denominator of 2 for the first term and a common denominator of 4 for the second term. To combine the terms, we need a common denominator. Let's find the least common multiple:

The least common multiple of 2 and 4 is 4.

To convert the first term to have a denominator of 4, we multiply both the numerator and denominator by 2:

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

Now, the expression becomes:

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

We can now combine the like terms:

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

Next, let's combine the z terms and the constant terms separately:

For the z terms: 2z/4 - 3/4z
To subtract, we need to find a common denominator of 4:
(2z - 3)/4z

For the constant terms: 4 - 3 = 1

So, the final simplified expression is:

(2z - 3)/4z + 1

Answer 2

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

To subtract the given expression, we need to distribute and simplify each term.

First, let's distribute the 1/2:
1/2(z+4) = 1/2 * z + 1/2 * 4 = 1/2z + 2

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

Now, we can rewrite the expression as:
1/2z + 2 - 3/4z - 3

To subtract fractions, the denominators must be the same. In this case, we need to find a common denominator for 2 and 4. The least common multiple of 2 and 4 is 4.

Let's convert 2 to have the same denominator:
2 * 2/2 = 4/2

Now the expression becomes:
1/2z + 4/2 - 3/4z - 3

Simplify the coefficients:
1/2z - 3/4z + 4/2 - 3

To combine like terms, we need to have the same denominator for the z terms. The least common multiple of 2 and 4 is 4.

Let's convert 1/2z to have the same denominator:
1/2z * 2/2 = 2/4z

Now the expression becomes:
2/4z - 3/4z + 4/2 - 3

Combine the z terms:
(2/4z - 3/4z) + 4/2 - 3 = (2z - 3z)/4 + 4/2 - 3 = -z/4 + 4/2 - 3

Simplify the coefficients:
-z/4 + 2 - 3

To add or subtract fractions, the denominators must be the same. In this case, -z/4 and 2 can be expressed over a common denominator of 4.

Rewriting 2 as a fraction:
2 = 8/4

Now the expression becomes:
-z/4 + 8/4 - 3

Combine the terms with the same denominator:
(-z + 8 - 12)/4 = (-z - 4)/4

The final simplified expression is:
-(z+4)/4, or you can also write it as -1/4(z+4)

Answer 3

[AI-generated answer — Explain Bot]

To subtract the expression 1/2(z+4) - 3(1/4z+1), you'll need to distribute the coefficients and simplify the terms.

First, distribute the coefficients:

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 substitute the distributed expressions back into the original expression:

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

Next, combine like terms by combining the "z" terms and the constant terms:

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

To add or subtract fractions, the denominators must be the same. In this case, the denominators are already 2 and 4, so we don't need to find a common denominator.

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

Combine the "z" terms:

[(2z - 3z)/4] - 1

Simplify:

(-z/4) - 1

To subtract the fractions, we need a common denominator of 4:

(-z - 4)/4

Therefore, the final answer is (-z - 4)/4.