I don't understand how to solve this problem:
In solving the equation (x + 3)(x + 1) = 48, Eric stated that the solution would be
x + 3 = 48 => x = 45or (x + 1) = 48 => x = 47 However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.
Eric is applying the zero principle to a non zero quantity.
Zero Principle: if AB=0, then A,or B, or both is zero.
Silly nonsense : if AB=C, then A, or B, equals C
To solve the equation (x + 3)(x + 1) = 48, we need to find the values of x that make the equation true. Let's solve it step by step:
Step 1: Expand the equation:
(x + 3)(x + 1) = 48
x^2 + x + 3x + 3 = 48
x^2 + 4x + 3 = 48
Step 2: Rearrange the equation to form a quadratic equation:
x^2 + 4x - 45 = 0
Step 3: Factorize the quadratic equation or use the quadratic formula to find the solutions:
(x + 9)(x - 5) = 0
By setting each factor equal to zero, we get two possible solutions:
x + 9 = 0 => x = -9
x - 5 = 0 => x = 5
Now, to determine if each solution works, we substitute them back into the original equation:
For x = -9:
(x + 3)(x + 1) = 48
(-9 + 3)(-9 + 1) = 48
(-6)(-8) = 48
48 = 48
For x = 5:
(x + 3)(x + 1) = 48
(5 + 3)(5 + 1) = 48
(8)(6) = 48
48 = 48
Both solutions x = -9 and x = 5 satisfy the original equation (x + 3)(x + 1) = 48. Therefore, Eric's initial statement was incorrect.
To help Eric understand better, you can explain that he made an error in the expansion of the equation. Instead of distributing both terms properly, he incorrectly multiplied the constants separately, resulting in incorrect solutions. It's important to double-check work and ensure all steps are followed correctly when solving equations.