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
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.
What is the correct answer? Show all steps using inverse operations to solve for x
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.
Show the work to check that your answer is correct.
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.
Carlos made a mistake when solving the equation 2x - 9 = 19. He correctly isolated the variable by adding 9 to both sides of the equation, which gave him 2x = 28. However, instead of dividing both sides by 2 to solve for x, he simply divided 28 by 2, which resulted in x = 14.
To verify his solution and determine if his answer is correct, Carlos could have performed a check by substituting his solution, x = 5, back into the original equation. If the equation holds true, then his answer is correct.
Let's perform the check:
Original Equation: 2x - 9 = 19
Substituting x = 5:
2(5) - 9 = 19
10 - 9 = 19
1 = 19
Since 1 is not equal to 19, the equation did not hold true. Therefore, Carlos's solution of x = 5 is incorrect. To find the correct solution, he should divide both sides of the equation 2x - 9 = 19 by 2:
2x - 9 = 19
2x = 19 + 9
2x = 28
x = 28 / 2
x = 14
Hence, the correct solution to the equation 2x - 9 = 19 is x = 14.