Solve each problem. If x represents the number of pennies in a ja...

Question

Solve each problem. If x represents the number of pennies in a jar in an applied problem, which of the following equations cannot be a correct equation for finding x? (Hint:Solve the equations and consider the solutions.)
A. 5x+3 =11
B.12x+6 =-4
C.100x =50(x+3)
D. 6(x+4) =x+24

Accepted Answer

Hey everyone here we are asked to find which of the following equations is the correct equation. To find the number of cents in a pocket. So to determine the correct solution here, the correct equation, we need to solve each equation for X. So starting with our first equation, which is equation A. We have three X plus five is equal to nine. So now again we need to solve for X. So we want to get X completely alone. This means we first need to subtract five from both sides and so we are left with three. X is equal to nine minus five. And simplifying we have three, X is equal to nine minus five which is just four. And now to get X completely alone, we need to get rid of the coefficient. So we need to divide both sides by three and we see that X is equal to four thirds. So for our first equation we find that X is equal to four thirds. Well it doesn't make sense that the number of sense is a fraction. We need the number of sense to be a whole number. So this first equation doesn't make sense and therefore is not the correct equation. So now we can move on to equation B which is two, X plus four is equal to 18. Again solving for X. We first need to to subtract four from both sides, so we have two X is equal to 18 minus four. Now simplifying we have two X is equal to 14. Now we need to get rid of the coefficient here. So we need to divide both sides by two. And we see that for equation b X is equal to seven. Well the solution of seven does make sense because we can have seven cents in a pocket. So this does seem like a viable equation here. But let's go ahead and check the last two equations. So moving on to equation see where we have 50 X is equal to 10 times the quantity of X plus nine. Now again we need to solve for X. So we first need to factor in this 10 on the right hand side. So doing this, we have 50 X is equal to 10 X plus 90. Now we need all of the X terms on one side of the equation. So we can subtract 10 X from both sides and we get 50 X minus 10, X is equal to 90. And now simplifying, we have 40 X is equal to 90. And now getting rid of the coefficient for X. We divide both sides by 40. And we see after simplifying that X is equal to 9/4. Now, again, just like equation A. We have a fraction as our answer for X. Well, again, that doesn't make sense. We cannot have a fraction of sense. So this equation does not is not the correct equation. And now just checking our last equation here, equation D where we have 32, the quantity of X plus five is equal to X plus 16. Now again solving for X. We first want to factor in the three on the left hand side. So doing this, we have three X plus 15 is equal to X plus 16. Now we want to get all of our X terms alone. So we can start by subtracting 15 from both sides. So we have three X is equal to X plus minus 15. Simplifying. We see that we have three X is equal to X plus one. Now we want all of our X terms on the same side of the equation. So we just need to subtract X from both sides and we are left with three. X minus X is equal to one. And now simplifying this equation three X minus X is just two. X is equal to one. And now we have to divide both sides by the coefficient which is two. So for this last equation we see that the solution, the number of sense is X is equal to one half and again we can't have a fraction. So this solution also doesn't make sense. And so now we can clearly see that the only solution that makes sense is the X is equal to seven from equation A. Therefore A is our final answer. Here is the correct equation. So three X plus five is equal to nine is our final solution. Thanks for watching. I hope you found this video helpful and I'll see you again next time

Solve each problem. If x represents the number of pennies in a jar in an applied problem, which of the following equations cannot be a correct equation for finding x? (Hint:Solve the equations and consider the solutions.) A. 5x+3 =11 B.12x+6 =-4 C.100x =50(x+3) D. 6(x+4) =x+24

Key Concepts

Linear Equations

Solution of an Equation

Identifying Extraneous Solutions

Watch next