Final Answer:
The equations 10(x-5)=-15 and 4+2(x-2)=9 have the same solution.
Step-by-step explanation:
To determine whether two equations have the same solution, we need to find a value of x that satisfies both equations simultaneously. In this case, we will use the method of substitution.
First, let's rewrite equation 10(x-5)=-15 in a more convenient form:
x-5 = -1.5 (dividing both sides by 10)
Next, let's substitute this value of x into equation 4+2(x-2) and see if it satisfies the equation:
4+2(-3.5) = -9
We can see that this value of x indeed satisfies both equations simultaneously, so they have the same solution. In other words, the value of x that satisfies both equations is -7.5 (rounded to two decimal places).
Now let's explain how we found this solution. When we substitute x-5 for x in equation 10(x-5)=-15, we get:
10(-1.5) = -15
Next, we simplify this expression by multiplying both sides by -1:
-150 = -150 (since -1 * -1 is 1)
We can see that this simplified expression is equivalent to the original expression, so we know that our substitution was correct. This means that the value of x that satisfies equation 10(x-5)=-15 is also a solution to equation 4+2(x-2)=9.