Question 198874
# 1


{{{2(x+4)+3x=12}}} Start with the given equation.



{{{2x+8+3x=12}}} Distribute.



{{{5x+8=12}}} Combine like terms on the left side.



{{{5x=12-8}}} Subtract {{{8}}} from both sides.



{{{5x=4}}} Combine like terms on the right side.



{{{x=(4)/(5)}}} Divide both sides by {{{5}}} to isolate {{{x}}}.



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Answer:


So the solution is {{{x=4/5}}} which in decimal form is {{{x=0.8}}}. 



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# 2



{{{(3/4)x-5=-17}}} Start with the given equation.



{{{4((3/cross(4))x)-4(5)=4(-17)}}} Multiply EVERY term by the LCD {{{4}}} to clear any fractions.



{{{3x-20=-68}}} Distribute and multiply.



{{{3x=-68+20}}} Add {{{20}}} to both sides.



{{{3x=-48}}} Combine like terms on the right side.



{{{x=(-48)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



{{{x=-16}}} Reduce.



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Answer:


So the solution is {{{x=-16}}}



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# 3



{{{2(m-3)=5(2m-6)}}} Start with the given equation.



{{{2m-6=10m-30}}} Distribute.



{{{2m=10m-30+6}}} Add {{{6}}} to both sides.



{{{2m-10m=-30+6}}} Subtract {{{10m}}} from both sides.



{{{-8m=-30+6}}} Combine like terms on the left side.



{{{-8m=-24}}} Combine like terms on the right side.



{{{m=(-24)/(-8)}}} Divide both sides by {{{-8}}} to isolate {{{m}}}.



{{{m=3}}} Reduce.



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Answer:


So the solution is {{{m=3}}} 




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When do you need to reverse the inequality sign when you solve an inequality?


Let's show why by example:



Let's say we have the inequality {{{1 < 10}}} (which is true; 1 is less than 10). Now divide both sides by a negative number (say -1) to get


{{{(1)/(-1) < (10)/(-1)}}}



{{{-1 < -10}}}



which is now false (-1 is NOT less than -10). So to correct this, we simply flip the inequality sign to get: {{{-1>-10}}} and now the inequality is true again.