How do you solve $- 2 \leq x - 7 \leq 11$ $-2<=x-7<=11$ ?

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Answer 1 · 2016-08-03T13:23:16

$x \in [5, 18]$ $x in [5, 18]$

The first thing to do here is get $x$ $x$ alone in the middle of the compound inequality by adding $7$ $7$ to all three sides

$-2 + 7 <= x - color(red)(cancel(color(black)(7))) <= 11 + 7$

$color(white)(aaaaa)5 <= color(white)(aa)xcolor(white)(aa) <= 18$

You now know that in order to be part of the solution interval, a value of $x$ must satisfy two conditions

$x >= color(white)(1)5 ->$ the left side of the compound inequality

$x <= 18 ->$ the right side of the compound inequality

For the first condition, you need $x$ to be greater than or equal to $5$ . In interval notation, this is written as

$x in [5, +oo)$

For the second condition, you need $x$ to be smaller than or equal to $18$ . In interval notation, this is written as

$x in (-oo, 18]$

This means that the solution interval for the compound inequality must have $x$ greater than or equal to $5$ and smaller than or equal to $18$ .

Thsi is written as

$x in (-oo, 18] nn [5, +oo) implies color(green)(|bar(ul(color(white)(a/a)color(black)( x in [5, 18])color(white)(a/a)|)))$

How do you solve -2<=x-7<=11−2≤x−7≤11-2<=x-7<=11?