Question 1094165
We'll use the rule that if {{{abs(x) < k}}} then {{{-k < x < k}}} where k is any positive number. 


For instance, if {{{abs(x) < 4}}} then {{{-4 < x < 4}}}. We can replace x with any algebraic expression and this rule will still work. 


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{{{abs(5x-2) < 9}}}


{{{-9 < 5x-2 < 9}}} Use the rule shown above


{{{-9+2 < 5x-2+2 < 9+2}}} Add 2 to all sides


{{{-7 < 5x < 11}}}


{{{-7/5 < 5x/5 < 11/5}}} Divide all sides by 5


{{{-7/5 < x < 11/5}}}


{{{-1.4 < x < 2.2}}}


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The answer, expressed in fraction form, is {{{-7/5 < x < 11/5}}}


In decimal form, the answer would be {{{-1.4 < x < 2.2}}}


The format will depend on your teacher.