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

( − ∞ , 7 ) \left(-\infty,7\right) ( − ∞ , 7 )

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

we're asked to write the following in interval notation. We're given the inequality that x is less than seven. Now thinking about values that are less than seven, this could be a value like 6.5, five, zero, negative two, negative a million. These are all values less than seven. So we need to account for this in our interval notation. So these values less than seven span all the way to negative infinity. So that means my interval here will go from negative infinity up until I reach seven. Now how should I enclose these values in parentheses or square brackets? Well, we always use parentheses for infinity because infinity is not an actual value that we can include. And what about our seven? Well, here we're looking at values that are less than seven, but not equal to seven. So I don't want to include that seven either, and I need to use parentheses here. And here's my inequality in interval notation, from negative infinity to seven. Let us know if you have questions, and I'll see you in the next one.

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

( − ∞ , 7 ) \left(-\infty,7\right) ( − ∞ , 7 )

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

[ 7 , ∞ ) \left\lbrack7,\infty\right) [ 7 , ∞ )

( 7 , ∞ ) \left(7,\infty\right) ( 7 , ∞ )

2. Linear Equations and Inequalities

Linear Inequalities in One Variable

Beginning & Intermediate Algebra

2. Linear Equations and Inequalities

Linear Inequalities in One Variable

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Multiple Choice

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

$\left(-\infty,7\right\rbrack$

$\left\lbrack7,\infty\right)$

$\left(7,\infty\right)$

$\left(-\infty,7\right)$

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 equal to 7, the interval will end at 7 with a parenthesis, not a bracket.

The other end of the interval extends indefinitely to the left, which is represented by negative infinity $-\infty$. Infinity is always represented with a parenthesis because it is not a number that can be reached or included.

Combine these observations to write the interval notation as $\left(-\infty,7\right)$, which means all real numbers less than 7.

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