How many solutions does the following equation have?
-14(z-5)=-14z+70−14(z−5)=−14z+70
To determine the number of solutions for the given equation, we will simplify the equation and solve for z.
-14(z - 5) = -14z + 70
Let's start by distributing -14 to the terms inside the parentheses on the left side.
-14z + 70 = -14z + 70
Now, we can see that the variable z is present on both sides of the equation, and all the terms are the same on both sides as well. This means that the equation has infinitely many solutions.
In general, if you end up with an equation where the variable cancels out, like in this case, and you end up with a true statement (e.g., 0 = 0, 5 = 5), it means that there are infinitely many solutions.