Final answer:
The solution to the algebraic equation -2v - 23 = -5(v + 7) is v = -4. After distributing, combining like terms, isolating the variable, and checking the solution, the correct value of v is verified.
Step-by-step explanation:
To solve the algebraic equation -2v - 23 = -5(v + 7), we first expand the right side of the equation by distributing the -5 across the parentheses. This simplifies the equation as follows:
-2v - 23 = -5v - 35
Next, we eliminate terms where possible to simplify the algebra. We can do this by adding 5v to both sides of the equation to get:
-2v + 5v - 23 = -5v + 5v - 35
v - 23 = -35
Now, to isolate the variable v, we add 23 to both sides of the equation:
v - 23 + 23 = -35 + 23
v = -12
After finding the value for v, we check to see if the answer is reasonable by substituting it back into the original equation:
-2(-12) - 23 = -5(-12 + 7)
24 - 23 = -5(-5)
1 = 25
Since the check does not result in a true statement, we can conclude that there was a mistake in our calculations. Let us revisit our steps. Actually, the correct solving step after adding 5v to both sides is:
3v - 23 = -35
Then, we add 23 to both sides:
3v = -12
Dividing both sides by 3, we get:
v = -4
This time, we check by substituting this correct value back into the original equation:
-2(-4) - 23 = -5(-4 + 7)
8 - 23 = -5(3)
-15 = -15
This statement is true, confirming that v = -4 is the correct solution.