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?
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
Thank you Farohw!
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.
OK what?
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
No problem! Let's work through it together.
To create an equation with infinitely many solutions, we need to ensure that no matter what value we assign to the variable, both sides of the equation will always be equal.
One example of such an equation is:
2x - x = x - 2x
To solve this equation, we can simplify it by combining like terms:
x = -x
Next, we want to isolate the variable on one side of the equation. To do that, we can subtract 'x' from both sides:
x + x = 0
2x = 0
Finally, dividing both sides of the equation by 2, we find:
x = 0
Now, let's analyze why this equation has infinitely many solutions. If we substitute the value of x = 0 back into the original equation, we get:
2(0) - (0) = (0) - 2(0)
0 - 0 = 0 - 0
0 = 0
Since 0 is equal to 0, the equation is true for any value of x. Therefore, the solution set is infinite, as any real number can be substituted for x and the equation will still hold true.