Simplify the following equation: 3x+4y=4x-7y
user
Sure, let's try to simplify this equation using mathematical operations allowed in algebra.

1. **Step 1:** Subtract 4x from both sides. This will give you:

   -3x + 4y = 4x - 7y - 4x

   **Note:** This is a pure number operation, which doesn't need any specific order, so we don't need to use parentheses ( ).

2. **Step 2:** Combine the two like terms (x and y) on the left-hand side of the equation.

   -3x + 4y = 4x - 7y - 4x

   becomes

   -3x + 4y = -3x - 7y

3. **Step 3:** Add (or subtract) the terms at both sides of the equation with a sign opposite to them. Or this case, we only have one such pair.

   -3x + 4y = -3x - 7y

   becomes

   -10y = -3x

   which is equivalent to 10y = 3x. This step is often called 'Combining like terms' when done with '+' sign.

4. **Step 4:** Swap the places of x and y.

   -10y = 3x

   becomes

   y = 3/10x

   Further, we can simplify this by multiplying both sides of this equation by 1/3.

   y = (3/10) * (10/3)x

   becomes

   y = (1/3) * x

   which is what we get on solving for y. 

So, the simplified form of this equation is,

   3x + 4y = 4x - 7y

     => y = (1/3) * x

And, this gives a slope-intercept form of a line in a graph. If a line is in the slope-intercept form, it's generally a straight line. A straight line in algebra terms is called a linear equation, and this linear equation tells us the slope and y-intercept of the line.
assistant
Simplify the following equation: 3x+4y=4x-7y
user
Sure, to simplify the equation, let's first move the terms involving the same variable to the same side of the equation.

Subtract 3x from both sides:

4y = 4x - 3x - 7y

This simplifies to:

4y = x - 7y

Now, add 7y to both sides:

4y + 7y = x

This simplifies to:

11y = x

So, the simplified form of the equation is x = 11y.
assistant