Finding a from the Equation 6a + 3w = p + 1

In this mathematical journey, we’ll solve for the variable ‘a’ in the equation 6a + 3w = p + 1. This type of equation often appears in various areas of science and mathematics. Knowing how to isolate ‘a’ provides us with valuable insights.

Step 1: Start with the Equation

Math: 6a + 3w = p + 1

Explanation: We start with the given equation. Our objective is to isolate ‘a’ on one side of the equation.

Step 2: Isolate 6a

Math: 6a = p + 1 – 3w

Explanation: We rearrange the equation by moving all terms that do not include ‘a’ to the other side. This isolates 6a.

Step 3: Solve for a

Math: a = (p + 1 – 3w) / 6

Explanation: We divide every term by 6, thus solving for ‘a’.

Step 4: Final Expression for a

Math: a = (p + 1 – 3w) / 6

Explanation: This is the final expression for ‘a’, in terms of ‘p’, ‘w’, and 1.

Conclusion

We have successfully solved for ‘a’ from the equation 6a + 3w = p + 1. This mathematical skill can be very useful in multiple areas of study.

Finding p from the Equation 6a + 3w = p + 1

Unveil the mysteries of algebra as we solve for the variable ‘p’ in the equation 6a + 3w = p + 1. This algebraic exercise is particularly useful for those delving into mathematics, engineering, or any field requiring analytical skills.

Step 1: Start with the Equation

Math: 6a + 3w = p + 1

Explanation: We start with the original equation. The goal is to isolate ‘p’ on one side.

Step 2: Move 1 to the Other Side

Math: p = 6a + 3w – 1

Explanation: To isolate ‘p’, we move the constant term 1 to the opposite side of the equation.

Step 3: Final Expression for p

Math: p = 6a + 3w – 1

Explanation: We’ve successfully isolated ‘p’, and this is our final expression for it in terms of ‘a’, ‘w’, and 1.

Conclusion

Our journey comes to an end as we successfully isolate ‘p’ in the equation 6a + 3w = p + 1. This is a fundamental skill in algebra that you’ll find useful in a wide array of applications.