How do you solve $- 5 < 2 (x - 4) \leq 6$ $-5< 2( x - 4) \leq 6$ ?

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Answer 1 · 2017-03-29T19:11:32

See the entire solution process below:

First, expand the term in parenthesis by multiplying each term in parenthesis by the term outside the parenthesis;

$- 5 < (2 \times x) - (2 \times 4) \leq 6$ $-5 < (2 xx x) - (2 xx 4) <= 6$

$- 5 < 2 x - 8 \leq 6$ $-5 < 2x - 8 <= 6$

Next, add $8$ $color(red)(8)$ to each segment of the inequality to isolate the $x$ $x$ term while keeping the system of inequalities balanced;

$- 5 + 8 < 2 x - 8 + 8 \leq 6 + 8$ $-5 + color(red)(8) < 2x - 8 + color(red)(8) <= 6 + color(red)(8)$

$3 < 2 x - 0 \leq 14$ $3 < 2x - 0 <= 14$

$3 < 2 x \leq 14$ $3 < 2x <= 14$

Next, divide each segment of the system by $2$ $color(red)(2)$ to solve for $x$ $x$ while keeping the inequalities balanced:

$\frac{3}{2} < \frac{2 x}{2} \leq \frac{14}{2}$ $3/color(red)(2) < (2x)/color(red)(2) <= 14/color(red)(2)$

$3/2 < (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) <= 7$

$3/2 < x <= 7$

How do you solve -5< 2( x - 4) \leq 6−5<2(x−4)≤6-5< 2( x - 4) \leq 6?