Write the following in interval notation.x≥0x\ge0

[ 0 , ∞ ) \left\lbrack0,\infty\right) [ 0 , ∞ )

Write the following in interval notation. x ≥ 0 x\ge0

Here we're asked to write the following in interval notation. We're given the inequality that x is greater than or equal to zero. So how can we write this in interval notation? Well, thinking about values that are greater than zero, these are values like one, two, three, a 100, a million. So we need to encompass all of those values using interval notation. So starting from zero, we're looking at any value greater than zero all the way to infinity. So I'm gonna write here zero comma infinity. Now should we use parentheses or square brackets on either side of this interval? Well, since x can be greater than or equal to zero, I wanna make sure that I include that zero by using a square bracket. But with our infinity, remember that infinity is not an actual value that we can include. So we wanna make sure that we use a parenthesis on that side of our interval. And here's our inequality in interval notation, from zero to infinity with that zero enclosed with a square bracket. Let me know if you have questions and let's keep going.

Write the following in interval notation. x ≥ 0 x\ge0

[ 0 , ∞ ) \left\lbrack0,\infty\right) [ 0 , ∞ )

( − ∞ , 0 ) \left(-\infty,0\right) ( − ∞ , 0 )

( 0 , ∞ ) \left(0,\infty\right) ( 0 , ∞ )

( − ∞ , 0 ] \left(-\infty,0\right\rbrack ( − ∞ , 0 ]

2. Linear Equations and Inequalities

Linear Inequalities in One Variable

Intermediate Algebra

2. Linear Equations and Inequalities

Linear Inequalities in One Variable

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Multiple Choice

Write the following in interval notation.
$x is greater than or equal to 0$

$\left(-\infty,0\right)$

$\left\lbrack0,\infty\right)$

$\left(0,\infty\right)$

$\left(-\infty,0\right\rbrack$

Verified step by step guidance

Identify the inequality given: $x \ge 0$. This means $x$ is greater than or equal to zero.

Recall that interval notation expresses all values of $x$ that satisfy the inequality as a continuous range.

Since $x$ can be equal to 0, use a square bracket '[' to include 0 in the interval.

Because $x$ can be any number greater than 0 extending to infinity, use a parenthesis ')' with $\infty$ to indicate it extends indefinitely and infinity is not included.

Combine these to write the interval notation as $\left[0, \infty\right)$, representing all $x$ values from 0 to infinity, including 0.

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