In the equation 3x = 4xy - 10, what can be solved for x?
Understand the Problem
The question is asking us to solve the equation $3x = 4xy - 10$ for the variable $x$. We will manipulate the equation to isolate $x$ on one side.
Answer
$$ x = \frac{10}{4y - 3} $$
Answer for screen readers
The solution for $x$ is
$$ x = \frac{10}{4y - 3} $$
Steps to Solve
- Rearrange the equation
Start with the original equation:
$$ 3x = 4xy - 10 $$
To isolate terms with $x$, move all terms involving $x$ to one side by adding $10$ to both sides:
$$ 3x + 10 = 4xy $$
- Factor out $x$
To make it easier to isolate $x$, notice that $x$ can be factored out on the right side. Rewrite the equation:
$$ 3x + 10 = x(4y) $$
- Isolate $x$
Now, we want to isolate $x$. To do this, subtract $3x$ from both sides:
$$ 10 = x(4y - 3) $$
- Solve for $x$
Finally, divide both sides by $(4y - 3)$, given that $4y - 3 \neq 0$:
$$ x = \frac{10}{4y - 3} $$
The solution for $x$ is
$$ x = \frac{10}{4y - 3} $$
More Information
This equation shows $x$ expressed in terms of $y$. This kind of manipulation is useful in algebra to express one variable in terms of another, especially in systems of equations or functions.
Tips
- Forgetting to move all terms involving $x$ to one side can lead to incorrect simplifications. Always check that you have isolated all $x$ terms properly before factoring.
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