Solve $5 p-3=15-4 p$
Answer (1)
Add 4 p to both sides: 9 p − 3 = 15 .
Add 3 to both sides: 9 p = 18 .
Divide both sides by 9 : p = 2 .
The solution is 2 .
Explanation
Understanding the Problem We are given the equation 5 p − 3 = 15 − 4 p and our goal is to find the value of p that makes this equation true.
Isolating the Variable Term To solve for p , we first want to get all the terms with p on one side of the equation and the constant terms on the other side. We can start by adding 4 p to both sides of the equation:
5 p − 3 + 4 p = 15 − 4 p + 4 p
This simplifies to:
9 p − 3 = 15
Isolating the Variable Next, we want to isolate the term with p . We can do this by adding 3 to both sides of the equation:
9 p − 3 + 3 = 15 + 3
This simplifies to:
9 p = 18
Solving for p Finally, to solve for p , we divide both sides of the equation by 9:
9 9 p = 9 18
This simplifies to:
p = 2
Verification To make sure our solution is correct, we can substitute p = 2 back into the original equation:
5 ( 2 ) − 3 = 15 − 4 ( 2 )
10 − 3 = 15 − 8
7 = 7
Since the equation holds true, our solution is correct.
Examples
Imagine you're trying to balance a seesaw. On one side, you have 5 bags of sand, but 3 pounds are missing. On the other side, you have 15 pounds, but 4 bags of sand are missing. Solving this equation helps you find the weight of each bag of sand so the seesaw is perfectly balanced. This type of problem is also useful in balancing chemical equations, calculating electrical circuits, or determining the break-even point in business.
