Carlos solved the equation below for x. His solution is x = 5. What mistake did Carlos make and how could he have verified his solution to know for certain that his answer is correct?
2x - 9 = 19
2x = 10
x = 5
Part C: What is the correct answer? Show all steps using inverse operations to solve for x. (10 pts)
2x - 9 = 19
The mistake Carlos made is in the second step. He incorrectly divided both sides of the equation by 2 instead of adding 9 to both sides first. The correct steps to solve the equation are as follows:
2x - 9 = 19
Add 9 to both sides:
2x - 9 + 9 = 19 + 9
2x = 28
Divide both sides by 2:
2x/2 = 28/2
x = 14
To verify the solution, Carlos could substitute the value of x back into the original equation and see if both sides are equal:
2(14) - 9 = 19
28 - 9 = 19
19 = 19
Since both sides of the equation are equal, the correct answer is indeed x = 14.