72.3k views
2 votes
Your friend says the solution to 4x 24x−5=7(4x 7) is x=54. solve 4x 24x−5=7(4x 7). what was your​ friend's likely​ error? question content area bottom part 1 solve 4x 24x−5=7(4x 7). select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. a. x= enter your response here b. the equation has infinitely many solutions. c. the equation has no solution.

User Ahmer Khan
by
7.9k points

1 Answer

3 votes

Final answer:

The likely error your friend made was a miscalculation or misinterpretation of the equation 4^x + 24x − 5 = 7(4^x + 7). The correct solution, after simplification and solving for x, is x = 2.25, not x = 54.

Step-by-step explanation:

First, let's identify your friend's likely error by solving the equation 4x + 24x−5 = 7(4x + 7). Notice that there seems to be a typographical error in the original expression provided. It appears the equation should be 4^x + 24x − 5 = 7(4^x + 7). Assuming this corrects the typo, we can start by simplifying the right side of the equation:

4^x + 24x − 5 = 28^x + 49

Next, we subtract 4^x and 49 from both sides to isolate the variable term:

24x − 5 − 4^x − 49 = 28^x + 49 − 4^x − 49

Which simplifies to:

24x − 54 = 0

Now, we can solve for x:

x = 54/24

x = 2.25

Thus, the correct solution is x = 2.25, not x = 54. To prevent such mistakes, it is important to carefully check each step of the algebraic process and eliminate terms where possible to simplify the equation.

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories