Question

$-\frac{3}{4}\left(5p-12\right)+2\left(8-\frac{1}{4}p\right)=$

Answer 1

To simplify the expression
`\((3)/(4)(5p-12)+2(8-(1)/(4)p)\)`, you must distribute terms and combine like terms to get the simplified expression
`\[ (13)/(4)p + 7 \]`.

Step-by-step explanation:

First, let's simplify the expression inside the parentheses and distribute the multiplication across the terms.

Given the expression:


`\[ (3)/(4)(5p - 12) + 2 \left( 8 - (1)/(4)p \right) \]`

Let's work on the first part,
`\( (3)/(4)(5p - 12) \)`:

Multiply 5p by
`\( (3)/(4) \)` to get
`\( (3)/(4) \cdot 5p = (15)/(4)p \)`.
Multiply (-12) by
`\( (3)/(4) \)` to get
`\( (3)/(4) \cdot -12 = -9 \)`.

So the first part simplifies to
`\( (15)/(4)p - 9 \)`.

Now the second part,
`\( 2 \left( 8 - (1)/(4)p \right) \)`:

Multiply 8 by 2 to get
`\( 2 \cdot 8 = 16 \)`.
Multiply
`\( -(1)/(4)p \)` by 2 to get
`\( 2 \cdot -(1)/(4)p = -(2)/(4)p \)` which simplifies to
`\( -(1)/(2)p \)`.

So the second part simplifies to
`\( 16 - (1)/(2)p \)`.

Now combining the simplified parts together:


`\[ (15)/(4)p - 9 + 16 - (1)/(2)p \]`

Next, let's combine like terms:


`\( (15)/(4)p - (1)/(2)p \)` can be combined by converting
`\( (1)/(2) \)` into quarters to get a common denominator. Since
`\( (1)/(2) = (2)/(4) \)`, we have
`\( (15)/(4)p - (2)/(4)p = (13)/(4)p \)`.
Combine the constants -9 + 16 to get 7.

So the simplified expression is:


`\[ (13)/(4)p + 7 \]`

This expression represents the simplified form without setting it equal to anything. If you have an equation to solve (meaning this expression should be equal to a certain value), please provide the complete equation for us to move forward with finding the value of p.