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
What mistake did Carlos make? Explain in detail
Carlos made a mistake when solving the equation. The error is in his third step, where he incorrectly isolated the variable x. In his third step, Carlos divided both sides of the equation by 2 to isolate x. However, he mistakenly divided the right side by 2 but not the left side.
To verify the solution, Carlos could have substituted the value of x back into the original equation and checked if it holds true. In this case, he would need to substitute x = 5 into the original equation 2x - 9 = 19.
When substituting x = 5 into the equation, we get:
2(5) - 9 = 19
10 - 9 = 19
1 = 19
This equation is false, indicating that Carlos' solution of x = 5 is incorrect.