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 2x. To verify his solution, Carlos could substitute x = 5 back into the original equation and check if it satisfies the equation. If it does, then his solution is correct.

what could he have done to check his aswer

To check his answer, Carlos could have substituted x = 5 back into the original equation and see if the equation holds true.

Plugging in x = 5 into the original equation:
2(5) - 9 = 19
10 - 9 = 19
1 = 19

Since the equation is not true when x = 5, Carlos made a mistake in his solution.

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

2x - 9 = 19

To solve the equation 2x - 9 = 19, we will use inverse operations to isolate the variable x.

First, we will add 9 to both sides of the equation:

2x - 9 + 9 = 19 + 9
2x = 28

Next, we will divide both sides of the equation by 2:

(2x)/2 = 28/2
x = 14

Therefore, the correct solution is x = 14.

An electrician charges $75 as a one-time fee plus an additional $45 per hour. If the total bill is $131.25, how many hours did it take for the electrician to complete the repair?

Let's assume the number of hours the electrician took to complete the repair is represented by "h".

The total bill is calculated as follows: one-time fee + (hourly rate * number of hours)

The equation that represents the given information is:
75 + 45h = 131.25

Now, we can solve this equation to find the value of h:

Subtract 75 from both sides:
45h = 131.25 - 75
45h = 56.25

Divide both sides by 45:
h = 56.25 / 45
h ≈ 1.25

Therefore, it took the electrician approximately 1.25 hours to complete the repair.

define the varibale for this problem

In this problem, the variable "h" represents the number of hours it took for the electrician to complete the repair.

Write an equation with the variable to represent the situation.

Let's use the variable "h" to represent the number of hours it took for the electrician to complete the repair.

The equation that represents the situation is:
75 + 45h = 131.25

In this equation, the one-time fee of $75 is added to the product of the hourly rate of $45 and the number of hours "h". The result should equal the total bill of $131.25.

Solve the equation. Show ALL work

We'll solve the equation step by step:

75 + 45h = 131.25

First, let's subtract 75 from both sides to isolate the term with "h" on the left side of the equation:

75 + 45h - 75 = 131.25 - 75

This simplifies to:

45h = 56.25

Next, let's divide both sides of the equation by 45 to solve for "h":

45h/45 = 56.25/45

This simplifies to:

h = 1.25

Therefore, the solution to the equation is h = 1.25. This means it took the electrician 1.25 hours to complete the repair.

If he arrived at 9:30 a.m., what time was he finished with the repair? Show calculations.

If the electrician arrived at 9:30 a.m. and it took him 1.25 hours to complete the repair, we can determine the time he finished by adding 1.25 hours to the start time.

To do this, we convert 1.25 hours into minutes:

1 hour = 60 minutes
0.25 hours = 0.25 * 60 minutes = 15 minutes

Now, we can add 1 hour and 15 minutes to the start time of 9:30 a.m.:

9:30 a.m. + 1 hour 15 minutes = 10:45 a.m.

Therefore, the electrician finished the repair at 10:45 a.m.