Question 251537

{{{25-(3x+7)<=2(x+3)+x}}} Start with the given inequality.



{{{25-3x-7<=2x+6+x}}} Distribute.



{{{-3x+18<=2x+6+x}}} Combine like terms on the left side.



{{{-3x+18<=3x+6}}} Combine like terms on the right side.



{{{-3x<=3x+6-18}}} Subtract {{{18}}} from both sides.



{{{-3x-3x<=6-18}}} Subtract {{{3x}}} from both sides.



{{{-6x<=6-18}}} Combine like terms on the left side.



{{{-6x<=-12}}} Combine like terms on the right side.



{{{x>=(-12)/(-6)}}} Divide both sides by {{{-6}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x>=2}}} Reduce.



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Answer:


So the solution is {{{x>=2}}} which looks like *[Tex \LARGE \left\{x\|x\ge2\right\}] in set builder notation.