Question

Are 1 and \(-4\) the solutions of \((x+1)(x-4)=0 ?\) Explain.

Short answer

No, neither 1 nor -4 are solutions to the equation \((x+1)(x-4)=0\).

Step-by-step solution

Substitute the first number

Let's begin by substituting 1 for \(x\) in the equation \((x+1)(x-4)=0\). Plugging in gives \((1+1)(1-4)=0\) which simplifies to \(2*(-3)=0\) that is \(-6=0\).

Analyze the result

As observed, substituting 1 does not make the equation hold, since the left hand side (-6) is not equal to zero. Thus, 1 is not a solution to this equation.

Substitute the second number

Now let's substitute \(-4\) for \(x\) in the equation \((x+1) (x-4)=0\). This now gives \((-4+1) * (-4-4) = 0\) which simplifies to \(-3*(-8) = 0\) or \(24=0\).

Analyze the result

As we see, substituting \(-4\) does not make the equation hold, as \(24\) is not equal to zero. Thus, \(-4\) is not a solution to this equation either.