Question

How do you solve `13- 3p = - 5( 3+ 2p )`?

Answer 1

`p = -4`

Explanation:

`13 - 3p = -5(3+2p)`

First, use the distributive property (shown below) to simplify `-5(3+2p)`:

Following this image, we know that:
`color(blue)(-5(3+2p) = (-5 * 3) + (-5 * 2p) = -15 - 10p)`

Put it back into the equation:
`13 - 3p = -15 - 10p`

Add `color(blue)(10p)` on both sides of the equation:
`13 - 3p quadcolor(blue)(+quad10p) = -15 - 10p quadcolor(blue)(+quad10p)`

`13 + 7p = -15`

Subtract `color(blue)13` from both sides:
`13 + 7p quadcolor(blue)(-quad13) = -15 quadcolor(blue)(-quad13)`

`7p = -28`

Divide both sides `color(blue)7`:
`(7p)/color(blue)7 = (-28)/color(blue)7`

Therefore,
`p = -4`

Hope this helps!

Answer 2

`p=-4`

Explanation:

We can distribute the `-5` on the right to get

`-3p+13=-15-10p`

We can start by adding `10p` to both sides to get

`7p+13=-15`

Next, to get our constants on one side, we can subtract `13` from both sides. We now have

`7p=-28`

To completely isolate the `p` term, we can divide both sides by `7`. We get

`p=-4`

Hope this helps!