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.