Question 172944
I'll do the first two to get you going in the right direction.



# 1




{{{3(x+2)-8=4(2-5x)+7}}} Start with the given equation.



{{{3x+6-8=8-20x+7}}} Distribute.



{{{3x-2=8-20x+7}}} Combine like terms on the left side.



{{{3x-2=-20x+15}}} Combine like terms on the right side.



{{{3x=-20x+15+2}}} Add {{{2}}} to both sides.



{{{3x+20x=15+2}}} Add {{{20x}}} to both sides.



{{{23x=15+2}}} Combine like terms on the left side.



{{{23x=17}}} Combine like terms on the right side.



{{{x=(17)/(23)}}} Divide both sides by {{{23}}} to isolate {{{x}}}.



----------------------------------------------------------------------


Answer:


So the answer is {{{x=17/23}}} which approximates to {{{x=0.739}}}. 




<hr>



# 2





{{{6x^2+7x=5}}} Start with the given equation.



{{{6x^2+7x-5=0}}} Subtract 5 from both sides.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=6}}}, {{{b=7}}}, and {{{c=-5}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(7) +- sqrt( (7)^2-4(6)(-5) ))/(2(6))}}} Plug in  {{{a=6}}}, {{{b=7}}}, and {{{c=-5}}}



{{{x = (-7 +- sqrt( 49-4(6)(-5) ))/(2(6))}}} Square {{{7}}} to get {{{49}}}. 



{{{x = (-7 +- sqrt( 49--120 ))/(2(6))}}} Multiply {{{4(6)(-5)}}} to get {{{-120}}}



{{{x = (-7 +- sqrt( 49+120 ))/(2(6))}}} Rewrite {{{sqrt(49--120)}}} as {{{sqrt(49+120)}}}



{{{x = (-7 +- sqrt( 169 ))/(2(6))}}} Add {{{49}}} to {{{120}}} to get {{{169}}}



{{{x = (-7 +- sqrt( 169 ))/(12)}}} Multiply {{{2}}} and {{{6}}} to get {{{12}}}. 



{{{x = (-7 +- 13)/(12)}}} Take the square root of {{{169}}} to get {{{13}}}. 



{{{x = (-7 + 13)/(12)}}} or {{{x = (-7 - 13)/(12)}}} Break up the expression. 



{{{x = (6)/(12)}}} or {{{x =  (-20)/(12)}}} Combine like terms. 



{{{x = 1/2}}} or {{{x = -5/3}}} Simplify. 



So the answers are {{{x = 1/2}}} or {{{x = -5/3}}}