Question

Jared believes this equation has one solution because the expressions on either side of the equal sign have different coefficients and different numbers of units. His work for simplifying the following equation is shown 5(y+4)=-3y-8+8y

What mistakes did Jared make if this equation actually has no solution?
a) He should have only distributed to the y.
b) He made a mistake with the negative when distributing.
c) He combined the like terms incorrectly.
d) He should have combined all terms to see if the expressions were equal.

Answer 1

Jared likely made a mistake by either combining like terms incorrectly or not combining all terms accurately. The correct process of distribution and combining terms reveals the equation has no solution because it reduces to the false statement 20=8.

Jared is attempting to solve the equation 5(y+4) = -3y - 8 + 8y. If Jared believes the equation has one solution, he may have made an error in his algebraic manipulations. The correct method to solve the equation involves distributing the 5 to both terms inside the parenthesis, combining like terms, and isolating the variable y. Let's examine the proper steps:

• Distribute the 5: 5y + 20 = 5y - 8 + 8y
• Combine like terms on the right side: 5y + 20 = 5y + 8
• Subtract 5y from both sides to get: 20 = 8

This final equation, 20=8, is not possible, which means the original equation has no solution. Jared's mistake could be in combining like terms incorrectly or not combining all terms. The correct conclusion is that an equation where the variable terms cancel out and leave a false statement indicates there is no solution.