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

[ 0 , ∞ ) \left\lbrack0,\infty\right)

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

( 0 , ∞ ) \left(0,\infty\right)

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

2. Linear Equations and Inequalities

Solving Linear Inequalities

Beginning Algebra

2. Linear Equations and Inequalities

Solving Linear Inequalities

Struggling with Beginning Algebra?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

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

$open paren negative infinity comma 0 close paren$

$open bracket 0 comma infinity close paren$

$open paren 0 comma infinity close paren$

$open paren negative infinity comma 0 close bracket$

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 uses brackets and parentheses to show whether endpoints are included or excluded. A square bracket $[$ or $]$ means the endpoint is included, while a parenthesis $( $ or $ )$ means it is not included.

Since $x$ is greater than or equal to zero, zero is included in the interval. Therefore, the interval will start with a square bracket at 0: $[0$.

The inequality has no upper bound, meaning $x$ can be any number greater than or equal to zero up to infinity. Infinity is always represented with a parenthesis because it is not a number that can be reached or included.

Combine these to write the interval notation as $[0, \infty)$, which means all numbers from zero (included) to infinity (not included).

3:43m

Watch next

Master Introduction to Linear Inequalities with a bite sized video explanation from Patrick Ford

Start learning