Solve for W 5w+9z=2z+3w
The Correct Answer and Explanation is:
To solve the equation (5w + 9z = 2z + 3w) for (w), we will isolate (w) on one side of the equation. Here’s a step-by-step breakdown of the solution:
- Start with the Original Equation:
[
5w + 9z = 2z + 3w
] - Rearrange the Equation:
To isolate the terms containing (w), we can move all the (w) terms to one side and the (z) terms to the other side. We do this by subtracting (3w) from both sides:
[
5w – 3w + 9z = 2z
]
Simplifying this gives:
[
2w + 9z = 2z
] - Isolate the (w) Terms:
Next, we need to isolate (2w). We can do this by subtracting (9z) from both sides:
[
2w = 2z – 9z
]
This simplifies to:
[
2w = -7z
] - Solve for (w):
To solve for (w), divide both sides of the equation by (2):
[
w = \frac{-7z}{2}
]
Thus, the solution for (w) in terms of (z) is:
[
w = -\frac{7}{2}z
]
Explanation:
In solving equations, the goal is to isolate the variable of interest (in this case, (w)) on one side of the equation while moving all other terms to the opposite side. The steps involved systematic rearrangement: first, moving like terms (those containing (w) together and those containing (z) together) using basic algebraic operations such as addition, subtraction, and division.
Initially, we had (5w) and (3w) on opposite sides. By combining these terms, we simplified the equation and made the manipulation easier. It’s essential to ensure that every operation done on one side of the equation is also performed on the other side to maintain the equation’s balance.
Ultimately, the solution expresses (w) in terms of (z), showing how changes in (z) directly affect (w). The negative coefficient indicates an inverse relationship; as (z) increases, (w) decreases, consistent with the algebraic operations performed.