Rewrite the following as an inequality statement. ( − ∞ , 2 ] \left(-\infty,2\right\rbrack

we're asked to rewrite the following as an inequality statement. We're given here the interval from negative infinity to two, with that negative infinity enclosed in a parenthesis and that two enclosed using a square bracket. So thinking about this interval going from negative infinity to two, how can we write this as an inequality? Well, any value spanning from negative infinity until we get to two, like say negative a million, zero, one, these are all values that are less than two. So I want x to be less than two. But this two is enclosed in a square bracket, which tells me that two is included in this interval, meaning that x could also be equal to two. So this inequality should be that x is less than or equal to two. So now we've rewritten our interval in inequality form. Let me know if you have any questions, and I'll see you in the next one.

2. Linear Equations and Inequalities

Linear Inequalities in One Variable

Beginning & Intermediate Algebra

2. Linear Equations and Inequalities

Linear Inequalities in One Variable

Struggling with Beginning & Intermediate Algebra?

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Multiple Choice

Rewrite the following as an inequality statement.
$open paren negative infinity comma 2 close bracket$

$x\le2$

$x<2$

$x\ge2$

$x>2$

Verified step by step guidance

Identify the interval notation given: $\left(-\infty, 2\right]$. This represents all values starting from negative infinity up to and including 2.

Recall that $-\infty$ is not a number but indicates that the values extend indefinitely to the left on the number line.

The square bracket $]$ at 2 means that 2 is included in the interval, so the inequality will use a 'less than or equal to' symbol.

Translate the interval into an inequality by letting $x$ represent any number in the interval. Since $x$ can be any number less than or equal to 2, write the inequality as $x \leq 2$.

Thus, the inequality statement equivalent to the interval $\left(-\infty, 2\right]$ is $x \leq 2$.

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Struggling with Beginning & Intermediate Algebra?

Rewrite the following as an inequality statement.(−∞,2]\left(-\infty,2\right\rbrack

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Rewrite the following as an inequality statement.
$open paren negative infinity comma 2 close bracket$