Question

Ali and Akari were trying to solve the equation: (x-1)(x-7)=5(x−1)(x−7)=5left parenthesis, x, minus, 1, right parenthesis, left parenthesis, x, minus, 7, right parenthesis, equals, 5 Ali said, "I'll multiply (x-1)(x-7)(x−1)(x−7)left parenthesis, x, minus, 1, right parenthesis, left parenthesis, x, minus, 7, right parenthesis and rewrite the equation as x^2-8x+7=5x 2 −8x+7=5x, squared, minus, 8, x, plus, 7, equals, 5. Then I'll subtract 555 from both sides, and use the quadratic formula with a=1a=1a, equals, 1, b=-8b=−8b, equals, minus, 8, and c=2c=2c, equals, 2." Akari said, "The left-hand side is factored, so I'll use the zero product property." Whose solution strategy would work?

Answer 1

Akari's strategy of using the zero product property would work in this case because the equation is already factored.

Step-by-step explanation:

To solve the equation (x-1)(x-7)=5, Ali's strategy involves expanding the equation and manipulating it to form a quadratic equation. He multiplies both sides of the equation by (x-1)(x-7) and simplifies it to x^2-8x+7=5. Then, he subtracts 5 from both sides to get x^2-8x+2=0. He wants to use the quadratic formula to find the solutions of the equation.

Akari's strategy, on the other hand, involves using the zero product property. Since the left-hand side of the equation is already factored as (x-1)(x-7), she can set each factor equal to zero and solve for x. This approach simplifies the problem and avoids the need for the quadratic formula.

Akari's strategy would work in this case because the equation is already factored. Instead of expanding and manipulating the equation as Ali did, Akari can directly set each factor equal to zero and solve for x.