Question 1094165
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could you please help me solve this equation 
|5x-2| < 9
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|5x-2| < 9.

Divide both sides by 5. You will get an equivalent inequality

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


The solution set to this inequality is the set of those x that are remoted less than {{{9/5}}} from the point {{{2/5}}} on the number line, i.e

the set of x,  {{{2/5 - 9/5}}} < x < {{{2/5+9/5}}},  or, which is the same,

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


<U>Answer</U>.  The solution set is the interval  ({{{-7/5}}},{{{11/5}}}) of the number line.
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