[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{1}{5}\left(x+1\frac{3}{4}\right)=-2\frac{1}{2} \end{gathered}$}[/tex]
Multiply both sides of the equation by 20, the lowest common denominator of 5,4,2.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4\left(x+\frac{4+3}{4}\right)=-10(2\times2+1) } \end{gathered}$}[/tex]
Add 4 and 3 to get 7.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4\left(x+\frac{7}{4}\right)=-10(2\times2+1) } \end{gathered}$}[/tex]
Use the distributive property to multiply −4 times x 4/7.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-4\times\left(\frac{7}{4}\right)=-10(2\times2+1) } \end{gathered}$}[/tex]
Multiply −4 by 4/7.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=10(2\times2+1) \ \ \to \ \ [Multiply \ 2\times2] } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=10(4+1) \ \ \to \ \ [Add] } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=10\times5 \ \ \to \ \ [Multiply] } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=-50 } \end{gathered}$}[/tex]
Add 7 to both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x=-50+7 \ \ \to \ \ [Add] } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x=-43 } \end{gathered}$}[/tex]
Divide both sides by −4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{x=\frac{-43}{-4} } \end{gathered}$}[/tex]
The fraction [tex]\bf{\frac{-43}{-4}}[/tex] can be simplified to [tex]\bf{\frac{43}{4}}[/tex] by removing the negative sign from the numerator and denominator.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{x=\frac{43}{4} } \end{gathered}$}[/tex]
simplify
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{x=10\frac{3}{4} \ \ \to \ \ \ Answer } \end{gathered}$}[/tex]
{ Pisces04 }
