Question

8. Write one equation that is equivalent to the equation 4x + y = 8.

Answer 1

Given the following equation

`4x+y=8`

We want to write an equivalent equation. When you do the same operation on both sides of an equation, the equal sign stays valid. Let's say we multiply both sides by two

`2\cdot(4x+y)=2\cdot(8)\Rightarrow8x+2y=16`

This equation is equivalent to the first one. Instead, we could've add three to both sides and then subtract 'y' from both sides.

`4x+y+3-y=8+3-y\Rightarrow4x+3=11-y`

And all of those equations are equivalent.

`4x+y=8\Leftrightarrow8x+2y=16\Leftrightarrow4x+3=11-y`