Compare Your Answers
Completion requirements
Solve the inequality \(x^2 - 2x \le 24\). Represent the solution set symbolically and on a number line.
Rearrange the inequality such that one side is zero.
\(\begin{align}
x^2 - 2x &\le 24 \\
x^2 - 2x - 24 &\le 0
\end{align}\)
Determine the zeros of the corresponding function.
\(\begin{align}
x^2 - 2x - 24 &= 0 \\
\left( {x - 6} \right)\left( {x + 4} \right) &= 0
\end{align}\)
The coefficient on \(x^2\) is positive, so the parabola will open up. Use the direction of opening and the zeros to sketch the graph.
The solution set is {\(x | -4 \le x \le 6, \thinspace x \in \rm{R}\)}.
Plot the solution set on a number line.
\(\begin{align}
x^2 - 2x &\le 24 \\
x^2 - 2x - 24 &\le 0
\end{align}\)
Determine the zeros of the corresponding function.
\(\begin{align}
x^2 - 2x - 24 &= 0 \\
\left( {x - 6} \right)\left( {x + 4} \right) &= 0
\end{align}\)
\(\begin{align}
x - 6 &= 0 \\
x &= 6
\end{align}\)
x - 6 &= 0 \\
x &= 6
\end{align}\)
\(\begin{align}
x + 4 &= 0 \\
x &= -4
\end{align}\)
x + 4 &= 0 \\
x &= -4
\end{align}\)
The coefficient on \(x^2\) is positive, so the parabola will open up. Use the direction of opening and the zeros to sketch the graph.
The solution set is {\(x | -4 \le x \le 6, \thinspace x \in \rm{R}\)}.
Plot the solution set on a number line.