Question

What are the steps to answer 3(d-8)-5=9(d+2)+1

Answer 1

First expand $3\left(d-8\right)-5$

$\mathrm{Distribute\:parentheses\:using}:\ \:a\left(b+c\right)=ab+ac$
$Where\; a=3,\:b=d,\:c=-8$

$3\cdot \:d+3\left(-8\right) \ \textgreater \ \mathrm{Apply\:minus-plus\:rules} \ \textgreater \ +\left(-a\right)=-a \ \textgreater \ 3d-3\cdot \:8$

$\mathrm{Multiply\:the\:numbers:}\:3\cdot \:8=24 \ \textgreater \ 3d-24 \ \textgreater \ 3d-24-5$

$\mathrm{Subtract\:the\:numbers:}\:-24-5=-29 \ \textgreater \ 3d-29$

Now expand $9\left(d+2\right)+1$

$\mathrm{Distribute\:parentheses\:using}:\ \:a\left(b+c\right)=ab+ac$
$Where\; a=9,\:b=d,\:c=2$

$9\cdot \:d+9\cdot \:2 \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:9\cdot \:2=18 \ \textgreater \ 9d+18$

$9d+18+1 \ \textgreater \ \mathrm{Add\:the\:numbers:}\:18+1=19 \ \textgreater \ 9d+19$

Now we have $3d-29=9d+19$

$\mathrm{Add\:}29\mathrm{\:to\:both\:sides} \ \textgreater \ 3d-29+29=9d+19+29 \ \textgreater \ \mathrm{Simplify}$

$3d=9d+48 \ \textgreater \ \mathrm{Subtract\:}9d\mathrm{\:from\:both\:sides} \ \textgreater \ 3d-9d=9d+48-9d$

$Simplify\;again\; \ \textgreater \ -6d=48 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}-6 \ \textgreater \ \frac{-6d}{-6}=\frac{48}{-6}$

$Simplify\;once\;more\;\ \textgreater \ d=-8$

Hope this helps!