Question

Andre is solving the equation 4(x+ 3/2 )=7. He says, "I can subtract 3/2 from each side to get 4x= 11/2 and then divide by 4 to get x= 11/8 ". Kiran says, "I think you made a mistake." How can Kiran know for sure that Andre's solution is incorrect?

Answer 1

Kiran can assure that Andre's solution is incorrect as Andre did not first distribute the 4 across the parentheses to both terms inside, which is a crucial step in algebraic rearrangement. After proper distribution and subtraction, dividing by 4 gives the correct solution, which is x = 1/4, not 11/8.

Step-by-step explanation:

Kiran can know for sure that Andre's solution is incorrect because of the improper application of algebraic rearrangement.

When solving the equation 4(x + 3/2) = 7, Andre incorrectly subtracted 3/2 from each side. Instead, one should first distribute the 4 across the parentheses to both terms inside.

Therefore, the correct steps would be to first multiply 4 by each term within the parentheses, resulting in 4x + 6 = 7. To isolate x, one must then subtract 6 from both sides, giving 4x = 1.

Dividing both sides by 4 would then yield x = 1/4, which is the correct solution.

Furthermore, understanding the relationship between multiplication and division and utilizing a common denominator would assist greatly in error-checking such solutions, as advised in algebraic operations.