Question

t+1/5-t-1=1/10 solve​

Answer 1

$\huge\color{lime}\ \boxed{\colorbox{black}{Answer : ♞ }}$

$\frac{ t+1 }{ 5-t-1 } = \frac{ 1 }{ 10 }$

SOLUTION:

$Variable \: t \: cannot \: be \: equal \: to \: \\ 4 \: since \: division \: by \: zero \: is \: not \\ defined. \: Multiply \: both \: sides \: of \\ the \: equation \: by \: 10\left(t-4\right), \: the \\ least \: common \: multiple \: of \: \\ 5-t-1,10.$

$= > \color{red} \: \: -10\left(t+1\right)=t-4$

$Use \: the \: distributive \: property \: to \: \\ multiply -10 \: by \: t+1.$

$= > \color{red}-10t-10=t-4$

$Subtract \: \: t \: \: from \: both \: sides.$

$= > \color{red}-10t-10-t=-4$

$Combine \: -10t \: and \: -t \: \: to \: get \: -11t.$

$= > \color{red}-11t-10=-4$

$Add \: 10 \: to \: both \: sides.$

$= > \color{red}-11t=-4+10$

$Add \: -4 \: and \: 10 \: to \: get \: 6.$

$= > \color{red}-11t=6$

$Divide \: both \: sides \: by \: -11.$

$= > \color{red}t=\frac{6}{-11}$

$Fraction \: \frac{6}{-11} \: can \: be \: rewritten \: \\ as -\frac{6}{11} \: by \: extracting \: the \: \\ negative \: sign.$

$= > \color{red}t=-\frac{6}{11}$

$\color{blue}t=-\frac{6}{11}\approx -0.545454545$