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

=
Nice!
Now there are no p terms on the left side of the equation. Next, let's try to get the p term, 7p, alone on the right side. How can you get rid of the 6 on the right side of the equation so that 7p is alone on the right while keeping the equation balanced?
20 − 2p
=
6 + 5p
+
2p
+
2p

20
=
6+7p

Add 6 to both sides

Subtract 6 from both sides

Subtract 7p from both sides
You got it!
Show that you can subtract 6 from both sides to get all of the numbers on the left while keeping the equation balanced.
20 − 2p
=
6 + 5p
+
2p
+
2p

20
=
6 + 7p
−

6
−

6
Nice!
Subtract 6 from both sides and rewrite the remaining values.
20 − 2p
=
6 + 5p
+
2p
+
2p

20
=
6 + 7p
−
6
−
6

Answer 1

Let's continue with the equation after the last operation:

You had:

\[ 20 = 6 + 7p - 6 \]

This simplifies to:

\[ 20 = 7p \]

Now, to isolate \( p \), you can divide both sides by 7:

\[ p = \frac{20}{7} \]

Thus, the value of \( p \) is \( \frac{20}{7} \), which is approximately \( 2.857 \).

To summarize the steps taken:

1. Started with the original equation: \( 20 - 2p = 6 + 5p \).
2. Added \( 2p \) to both sides: \( 20 = 6 + 7p \).
3. Subtracted \( 6 \) from both sides to isolate the \( p \) term: \( 20 - 6 = 7p \).
4. Simplified to: \( 14 = 7p \).
5. Divided by \( 7 \) to solve for \( p \): \( p = \frac{20}{7} \).

So, the solution is:

Value of \( p \): \( \frac{20}{7} \).