tell whether each equation has one solution, zero solutions or infinite solutions
5(x-3)+6=5x-9
If when you solve, the x's cancel and you are left with something like 5=5 that means there are an infinite number of solutions. This means that any number you choose will work. If you are left with something false like 0 =5, then there are no solutions.
5x -15 + 6 = 5x - 9
-9 = -9 True.. Infinite number of solutions.
Try substituting "0", "1", "10" and you will see that all three work.
Well, let's see if I can solve this equation without clowning around.
I'll simplify it step by step:
5(x-3) + 6 = 5x - 9
Using the distributive property:
5x - 15 + 6 = 5x - 9
Combining like terms:
5x - 9 = 5x - 9
Oops! It looks like both sides of the equation are equal. This means that every value of x will work!
Therefore, the equation has infinite solutions. Isn't that "solution-ly" awesome?
To determine whether the equation 5(x-3)+6=5x-9 has one solution, zero solutions, or infinite solutions, we can start by simplifying the equation.
First, distribute the 5 to the terms inside the parentheses:
5x - 15 + 6 = 5x - 9
Next, simplify the equation by combining like terms:
5x - 9 = 5x - 9
Now, we can see that both sides of the equation are the same, which means that the equation is an identity and it will have infinite solutions.
Therefore, the equation 5(x-3)+6=5x-9 has infinite solutions.
To determine whether the equation 5(x-3)+6=5x-9 has one solution, zero solutions, or infinite solutions, we need to simplify the equation and check the resulting expression.
Let's start by simplifying both sides of the equation:
5(x-3) + 6 = 5x - 9
Using the distributive property, we can multiply 5 with each term inside the parentheses:
5x - 15 + 6 = 5x - 9
Combining like terms:
5x - 9 = 5x - 9
Now, let's analyze the equation. We have the same term (5x) on both sides of the equation. Since subtracting 5x from both sides cancels out the x term completely, we end up with:
-9 = -9
In this case, both sides of the equation are equal (-9 = -9). This implies that the equation has infinite solutions.
To reach this conclusion, we simplified the equation and ended up with the statement -9 = -9. This indicates that any value of x would satisfy the original equation. Therefore, the equation 5(x-3)+6=5x-9 has infinite solutions.