Questions: Solve the inequality, and graph the solution set. (x+8)(x-1)<0

Solution Steps

To solve the inequality \((x+8)(x-1)<0\), we need to find the intervals where the product of \((x+8)\) and \((x-1)\) is negative.

1. Find the roots of the equation \((x+8)(x-1)=0\): \[ x+8=0 \implies x=-8 \] \[ x-1=0 \implies x=1 \]

2. Determine the sign of the product in the intervals defined by the roots:

   • For \(x < -8\), both \((x+8)\) and \((x-1)\) are negative, so their product is positive.
   • For \(-8 < x < 1\), \((x+8)\) is positive and \((x-1)\) is negative, so their product is negative.
   • For \(x > 1\), both \((x+8)\) and \((x-1)\) are positive, so their product is positive.

3. The solution to the inequality \((x+8)(x-1)<0\) is: \[ -8 < x < 1 \]

Final Answer