Write the following in interval notation.x<7x<7

( − ∞ , 7 ) \left(-\infty,7\right)

Write the following in interval notation. x < 7 x<7

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 < 7 x<7

( − ∞ , 7 ) \left(-\infty,7\right)

( − ∞ , 7 ] \left(-\infty,7\right\rbrack

[ 7 , ∞ ) \left\lbrack7,\infty\right)

( 7 , ∞ ) \left(7,\infty\right)

2. Linear Equations and Inequalities

Solving Linear Inequalities

Beginning Algebra

2. Linear Equations and Inequalities

Solving Linear Inequalities

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Multiple Choice

Write the following in interval notation.
$x is less than 7$

$open paren negative infinity comma 7 close bracket$

$open bracket 7 comma infinity close paren$

$open paren 7 comma infinity close paren$

$open paren negative infinity comma 7 close paren$

Verified step by step guidance

Identify the inequality given: $x < 7$. This means $x$ can be any number less than 7, but not equal to 7.

Recall that in interval notation, parentheses $(\ )$ are used to indicate that an endpoint is not included, while brackets $[\ ]$ indicate the endpoint is included.

Since $x$ can be any number less than 7 but not 7 itself, the interval will not include 7, so we use a parenthesis at 7.

The inequality $x < 7$ extends indefinitely to the left, so the lower bound is negative infinity, which is always represented with a parenthesis because infinity is not a number that can be included.

Combine these observations to write the interval notation as $\left(-\infty,7\right)$, which means all numbers less than 7 but not including 7.

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