x - 6y = -30
Understand the Problem
The question provides a linear equation with two variables (x and y). It seems to be asking either to solve for one variable in terms of the other, or to find solutions (x, y) that satisfy the equation. Without further instructions, I will assume the task is to express x in terms of y.
Answer
$x = \frac{7 - 4y}{3}$
Answer for screen readers
$x = \frac{7 - 4y}{3}$
Steps to Solve
- Isolate the term with x
To isolate the term with x, we need to subtract $4y$ from both sides of the equation: $$3x + 4y = 7$$ $$3x + 4y - 4y = 7 - 4y$$ $$3x = 7 - 4y$$
- Solve for x
To solve for $x$, divide both sides of the equation by 3: $$\frac{3x}{3} = \frac{7 - 4y}{3}$$ $$x = \frac{7 - 4y}{3}$$
$x = \frac{7 - 4y}{3}$
More Information
The equation $x = \frac{7 - 4y}{3}$ expresses $x$ in terms of $y$. For any value of $y$, you can substitute it into the equation to find the corresponding value of $x$ that satisfies the original equation $3x + 4y = 7$.
Tips
A common mistake is to incorrectly apply the order of operations when isolating $x$. For example, some might try to divide only a part of the right side of the equation by 3, such as writing $x = 7 - \frac{4y}{3}$, which is incorrect. Remember to divide the entire expression $(7 - 4y)$ by 3.
Another common mistake is to incorrectly move the $4y$ term to the other side of the equation. Remember that when moving a term from one side of the equation to the other, you must change its sign.
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