Question 165615
{{{(1/2)t-6+8(t-9+7)=4t*3-5+2+(3/4)t}}} Start with the given equation



{{{(1/2)t-6+8(t-9+7)=12t-5+2+(3/4)t}}} Multiply



{{{(1/2)t-6+8t-72+56=12t-5+2+(3/4)t}}} Distribute.



{{{4((1/cross(2))t-6+8t-72+56)=4(12t-5+2+(3/cross(4))t)}}} Multiply both sides by the LCD {{{4}}} to clear any fractions.



{{{2t-24+32t-288+224=48t-20+8+3t}}} Distribute and multiply.



{{{-88+34t=48t-20+8+3t}}} Combine like terms on the left side.



{{{-88+34t=-12+51t}}} Combine like terms on the right side.



{{{34t=-12+51t+88}}} Add {{{88}}} to both sides.



{{{34t-51t=-12+88}}} Subtract {{{51t}}} from both sides.



{{{-17t=-12+88}}} Combine like terms on the left side.



{{{-17t=76}}} Combine like terms on the right side.



{{{t=(76)/(-17)}}} Divide both sides by {{{-17}}} to isolate {{{t}}}.



{{{t=-76/17}}} Reduce.



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Answer:


So the answer is {{{t=-76/17}}} which approximates to {{{t=-4.471}}}.