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.

Question

2x - 9 = 19
2x = 10
x = 5

Answer 1

Carlos made a mistake when he divided both sides of the equation by 2 in order to isolate the variable x. The correct steps would be as follows:

2x - 9 = 19
2x = 19 + 9 (adding 9 to both sides)
2x = 28 (simplifying)
x = 28/2 (dividing both sides by 2)
x = 14

To verify his solution, Carlos could substitute the value of x (14) back into the original equation:

2(14) - 9 = 19
28 - 9 = 19
19 = 19

Since the equation is true when x = 14, Carlos can be certain that his original solution x = 5 is incorrect.

Answer 2

What is the correct answer? Show all steps using inverse operations to solve for x

Answer 3

To solve for x correctly, we need to apply inverse operations to isolate the variable x. Here are the correct steps:

1. Start with the equation: 2x - 9 = 19.

2. Add 9 to both sides of the equation to isolate the term with x: 2x - 9 + 9 = 19 + 9.
Simplifying, we get: 2x = 28.

3. Divide both sides of the equation by 2 to solve for x: 2x/2 = 28/2.
Simplifying, we get: x = 14.

Therefore, the correct solution to the equation is x = 14.

Answer 4

Show the work to check that your answer is correct.

Answer 5

To verify that the solution x = 14 is correct, we substitute this value back into the original equation and check if both sides are equal:

Original equation: 2x - 9 = 19.

Substituting x = 14:
2(14) - 9 = 19.
28 - 9 = 19.
19 = 19.

Since both sides of the equation are equal, we can conclude that the solution x = 14 is correct.