Question

Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions.


I have no idea?

Answer 1

The same variable on both sides?

If not, just any linear equation with two variables will work, such as

2x+3 = y-7

You can pick any value for x (or y) and find a solution for the other variable.

Answer 2

OK what?

Answer 3

if it has to be the same variable on both sides try something like:

7x + 1 = 3x + 5 + 4x -4

in other words
0 x = 0

Answer 4

Try, 3x + 5 = 3x + 5

As you can see the equation is equal to itself and if you subtract 3x from both sides you will get 5 = 5. The idea behind infinite solutions is that no matter what number you use for the variable, in this case x, the answer will always be true.

Let x = -4

So, 3x + 5 = 3x + 5

3(-4) + 5 = 3(-4) +5

-7 = -7

Answer 5

Thank you Farohw!