## Related questions with answers

Question

Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line.

$x^2 \leq 1$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 6Let's define the following inequality

$\begin{align*} x^2\leq1 \end{align*}$

To solve it, let's express the given inequality as a product of the two factors. Thus, let's consider the following

$\begin{align*} x^2&\leq1&& \textbf{Set inequality.} \\ x^2-1&\leq0 &&\textbf{Subtract $1$.}\\ (x-1)(x+1)&\leq0&&\textbf{Identity: $x^2-1=(x-1)(x+1)$.} \end{align*}$

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