How do you solve and write the following in interval notation: $2x + 6 < 8$ ?

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Answer 1 · 2018-03-18T14:33:56

See a solution process below:

First subtract $color(red)(6)$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$2x + 6 - color(red)(6) < 8 - color(red)(6)$

$2x + 0 < 2$

$2x < 2$

Now, divide each side of the inequality be $color(red)(2)$ to solve for $x$ while keeping the inequality balanced:

$(2x)/color(red)(2) < 2/color(red)(2)$

$(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 1$

$x < 1$

Or, in interval notation:

$(-oo, 1)$

How do you solve and write the following in interval notation: 2x + 6 < 82x + 6 < 8?