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. (3 points)
I need help with this one too. Thank you! :)
oops I spelled again incorrectly!!
please help soon! I want to finish this by today so that I can move on!!! please somebody help me!! Ms. Sue!!!
x=x
anything on the left will equal the right
infinite solutions
Sure! To create an equation with infinitely many solutions and solve it, let's consider the following equation:
2x + 4 = x + 6
To solve this equation, we want to isolate the variable on one side of the equation. Let's do that step by step:
Step 1: Start by subtracting "x" from both sides of the equation to eliminate the variables on both sides.
2x + 4 - x = x + 6 - x
This simplifies to:
x + 4 = 6
Step 2: Next, subtract 4 from both sides of the equation to isolate the variable on one side.
x + 4 - 4 = 6 - 4
This simplifies to:
x = 2
Now, we have solved the equation and found x = 2. But why does it have infinitely many solutions?
When we look at the original equation 2x + 4 = x + 6, we notice that we were able to isolate the variable and solve for it. However, when we simplify the equation, we realize that the variable "x" was eliminated from both sides of the equation. This means that any value of "x" that we substitute back into the equation will satisfy it.
In other words, for any value of "x" that we choose, the left side will always equal the right side of the equation. As a result, the equation has infinitely many solutions because any real number we substitute in for "x" will satisfy the equation.
Therefore, the equation 2x + 4 = x + 6 has infinitely many solutions.