How do you solve $-2\leq 3x + 4< 13$ ?

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Answer 1 · 2017-06-12T02:43:32

See a solution process below:

First, subtract $color(red)(4)$ from each segment of the system of inequalities to isolate the $x$ term while keeping the system balanced:

$-2 - color(red)(4) <= 3x + 4 - color(red)(4) < 13 - color(red)(4)$

$-6 <= 3x + 0 < 9$

$-6 <= 3x < 9$

Now, divide each segment by $color(red)(3)$ to solve for $x$ while keeping the system balanced:

$-6/color(red)(3) <= (3x)/color(red)(3) < 9/color(red)(3)$

$-2 <= (color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) < 3$

$-2 <= x < 3$

Or

$x >= -2$ and $x < 3$

Or, in interval notation:

$[-2, 3)$

How do you solve -2\leq 3x + 4< 13-2\leq 3x + 4< 13?