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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.
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
Bruh... just chill. People come here to get HELP!!! Not to hear crap from people like you.
Sorry No Name, I am not a troll and do not want to start a flame war.
Sure! Let's start by writing an equation with a variable on both sides of the equal sign. One example is:
2x - 7 = x + 3
To solve this equation, we want to isolate the variable x on one side of the equation by performing arithmetic operations on both sides. Let's take a look at the steps:
Step 1: Start with the given equation: 2x - 7 = x + 3.
Step 2: Subtract x from both sides of the equation to eliminate the variable terms on the right side of the equal sign: 2x - x - 7 = x - x + 3. Simplifying, we have: x - 7 = 3.
Step 3: Add 7 to both sides of the equation to isolate the variable term on the left side of the equal sign: x - 7 + 7 = 3 + 7. Simplifying further gives us: x = 10.
Now, let's analyze why this equation has infinitely many solutions. In this case, since we ended up with a single value for the variable (x = 10), it might seem like there is only one solution. However, if we substitute this value back into the original equation, we can see that it still holds true.
For instance, substituting x = 10 into the equation 2x - 7 = x + 3 gives us: 2(10) - 7 = 10 + 3, which simplifies to: 20 - 7 = 13. This equality is true, which means that any value of x = 10 will satisfy the equation.
In other words, no matter what value we choose for x, the equation 2x - 7 = x + 3 will always be true. Therefore, there are infinitely many solutions because any number can be substituted for x, and the equation will still hold.