Solve the equation below, where there are p terms on both sides of the equation. What’s the value of p?

Question

There are many ways to solve this equation. We're trying to get p alone on one side of the equation, equal to some number. We can start by first trying to get all of the p terms on the right. What move can you make first to get rid of the −2p on the left so that all of the p terms are on the right side of the equation?
20−2p=6+5p

Add 2p to both sides

Subtract 2p from both sides

Add 6 and 5p on the right
Nice!
Show that you can add 2p to both sides of the equation so that all of the p terms are on the right and the equation is balanced.
20 − 2p
=
6 + 5p
+

2p
+

2p
Nice!
Add 2p to both sides, then rewrite the equation to represent the remaining values.
20 − 2p
=
6 + 5p
+
2p
+
2p

=

Answer 1

Let's start with the given equation:

\[ 20 - 2p = 6 + 5p \]

Now, as suggested, we will add \(2p\) to both sides of the equation.

Doing this gives us:

\[ 20 - 2p + 2p = 6 + 5p + 2p \]

This simplifies to:

\[ 20 = 6 + 7p \]

Now we have moved all the \(p\) terms to the right side of the equation. Next, we can rewrite the equation:

\[ 20 = 6 + 7p \]

So, we can now see that all terms involving \(p\) are on the right side of the equation. The remaining values are \(20\) on the left and \(6\) on the right, along with the \(7p\) term.

To find the value of \(p\), we can continue solving the equation:

1. Subtract \(6\) from both sides:

\[ 20 - 6 = 7p \]

This simplifies to:

\[ 14 = 7p \]

2. Now, divide both sides by \(7\):

\[ p = \frac{14}{7} \]

This gives us:

\[ p = 2 \]

Therefore, the value of \(p\) is \(2\).