To solve for \( x \) in terms of \( y \) in the equation \( 7y - 4x \cdot 14 = 3x \), let's follow these steps:

### Step 1: Simplify the equation
First, simplify the equation by distributing and combining like terms if necessary.

Given:
\[
7y - 4x \cdot 14 = 3x
\]

Simplify \( -4x \cdot 14 \):
\[
7y - 56x = 3x
\]

### Step 2: Isolate the terms with \( x \)
Move the \( x \) terms to one side of the equation:
\[
7y = 3x + 56x
\]

Combine like terms:
\[
7y = 59x
\]

### Step 3: Solve for \( x \)
Divide both sides of the equation by 59 to isolate \( x \):
\[
x = \frac{7y}{59}
\]

So, \( x \) in terms of \( y \) is:
\[
\boxed{x = \frac{7y}{59}}
\]

Would you like more details on any part of the solution, or do you have any questions?

Here are 5 related questions you might find helpful:
1. How do you solve for \( y \) in terms of \( x \) in similar equations?
2. What happens if the coefficients of \( x \) and \( y \) are both negative?
3. Can you solve a system of equations involving similar terms?
4. How does the method change if the equation is quadratic in nature?
5. How do you interpret solutions in word problems that use these types of equations?

**Tip:** Always ensure you combine like terms before attempting to isolate the variable you're solving for. This simplifies the process and reduces errors.

Learn how to solve for x in terms of y in the equation 7y - 4x * 14 = 3x step-by-step. This problem involves linear equations and algebraic manipulation. Suitable for Grades 7-9 students learning algebraic techniques.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation