How do you solve and graph $- 7 < 6 x - 1 < 5$ $-7<6x-1<5$ ?

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Answer 1 · 2017-08-08T02:44:48

See a solution process below:

First, add $1$ $color(red)(1)$ to each segment of the system of inequalities to isolate the $x$ $x$ term while keeping the system balanced:

$- 7 + 1 < 6 x - 1 + 1 < 5 + 1$ $-7 + color(red)(1) < 6x - 1 + color(red)(1) < 5 + color(red)(1)$

$- 6 < 6 x - 0 < 6$ $-6 < 6x - 0 < 6$

$- 6 < 6 x < 6$ $-6 < 6x < 6$

Now, divide each segment by $6$ $color(red)(6)$ to solve for $x$ $x$ while keeping the equation balanced:

$- \frac{6}{6} < \frac{6 x}{6} < \frac{6}{6}$ $-6/color(red)(6) < (6x)/color(red)(6) < 6/color(red)(6)$

$-1 < (color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6)) < 1$

$-1 < x < 1$

Or

$x > -1$ and $x < 1$

Or, in interval notation:

$(-1, 1)$

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How do you solve and graph -7<6x-1<5−7<6x−1<5-7<6x-1<5?