Question

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.

Answer 1

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.