Final answer:
The solution to the equation 5x - 44 = 7(x - 8) is x = 6. This was determined by distributing the 7 on the right, eliminating terms to combine like terms, and isolating x to solve for its value. Upon checking, the solution was confirmed to be reasonable.
Step-by-step explanation:
To simplify the equation 5x - 44 = 7(x - 8), we must first distribute the 7 on the right side of the equation:
5x - 44 = 7x - 56
Next, eliminate terms to simplify the algebra by subtracting 5x from both sides:
-44 = 2x - 56
Then add 56 to both sides to isolate the variable term:
12 = 2x
Finally, divide both sides by 2 to solve for x:
x = 6
After solving, it's important to check the answer to ensure it is reasonable. Plugging the value of x back into the original equation:
5(6) - 44 = 7(6 - 8)
30 - 44 = 7(-2)
-14 = -14
The solution x = 6 is correct, as both sides of the original equation are equal when x is 6, which verifies our solution.