Question

What is the solution to this equation? -1/5(x+1 1/4)=-2 1/2

Answer 1

$\large\displaystyle\begin{gathered}\sf -\frac{1}{5}\left(x+1\frac{3}{4}\right)=-2\frac{1}{2} \end{gathered}$

Multiply both sides of the equation by 20, the lowest common denominator of 5,4,2.

$\large\displaystyle\text{ \begin{gathered}\sf \bf{-4\left(x+\frac{4+3}{4}\right)=-10(2\times2+1) } \end{gathered} }$

Add 4 and 3 to get 7.

$\large\displaystyle\text{ \begin{gathered}\sf \bf{-4\left(x+\frac{7}{4}\right)=-10(2\times2+1) } \end{gathered} }$

Use the distributive property to multiply −4 times x 4/7.

$\large\displaystyle\text{ \begin{gathered}\sf \bf{-4x-4\times\left(\frac{7}{4}\right)=-10(2\times2+1) } \end{gathered} }$

Multiply −4 by 4/7.

$\large\displaystyle\begin{gathered}\sf \bf{-4x-7=10(2\times2+1) \ \ \to \ \ [Multiply \ 2\times2] } \end{gathered}$

$\large\displaystyle\begin{gathered}\sf \bf{-4x-7=10(4+1) \ \ \to \ \ [Add] } \end{gathered}$

$\large\displaystyle\begin{gathered}\sf \bf{-4x-7=10\times5 \ \ \to \ \ [Multiply] } \end{gathered}$

$\large\displaystyle\begin{gathered}\sf \bf{-4x-7=-50 } \end{gathered}$

Add 7 to both sides.

$\large\displaystyle\begin{gathered}\sf \bf{-4x=-50+7 \ \ \to \ \ [Add] } \end{gathered}$

$\large\displaystyle\begin{gathered}\sf \bf{-4x=-43 } \end{gathered}$

Divide both sides by −4.

$\large\displaystyle\text{ \begin{gathered}\sf \bf{x=\frac{-43}{-4} } \end{gathered} }$

The fraction $\bf{\frac{-43}{-4}}$ can be simplified to $\bf{\frac{43}{4}}$ by removing the negative sign from the numerator and denominator.

$\large\displaystyle\text{ \begin{gathered}\sf \bf{x=\frac{43}{4} } \end{gathered} }$

simplify

$\large\displaystyle\text{ \begin{gathered}\sf \bf{x=10\frac{3}{4} \ \ \to \ \ \ Answer } \end{gathered} }$

{ Pisces04 }

Answer 2

Answer:

$\sf c)\ x=10\dfrac{3}{4}$

Step-by-step explanation:

Given equation:

$\sf -\dfrac{1}{5}\left(x+1\dfrac{3}{4}\right)=-2\dfrac{1}{2}$

Step 1: Convert the mixed numbers into improper fractions.

$\sf -\dfrac{1}{5}\left(x+\dfrac{4\times1+3}{4}\right)=-\dfrac{2\times2+1}{2}\implies -\dfrac{1}{5}\left(x+\dfrac{7}{4}\right)=-\dfrac{5}{2}$

Step 2: Distribute -⅕ through the parentheses.

$\sf-\dfrac{1}{5}(x)+-\dfrac{1}{5}\left(\dfrac{7}{4}\right)=-\dfrac{5}{2}\\\\\implies -\dfrac{1}{5}x-\dfrac{7}{20}=-\dfrac{5}{2}$

Step 3: Rewrite the equation with a common denominator of 20.

$\sf -\dfrac{1\times4}{5\times4}x-\dfrac{7}{20}=-\dfrac{5\times10}{2\times10}\\\\\implies -\dfrac{4}{20}x-\dfrac{7}{20}=-\dfrac{50}{20}$

Step 4: Multiply both sides by 20.

$\sf 20\left(-\dfrac{4}{20}x\right)-20\left(\dfrac{7}{20}\right)=20\left(-\dfrac{50}{20}\right)\\\\\implies -4x-7=-50$

Step 5: Add 7 to both sides.

$\sf -4x-7+7=-50+7\\\\\implies -4x=-43$

Step 6: Divide both sides by -4.

$\sf \dfrac{-4x}{-4}=\dfrac{-43}{-4}\\\\\implies x=\dfrac{43}{4}$

Step 7: Convert the answer back into a mixed number.

$\sf x=\dfrac{43}{4}\implies x=\dfrac{40+3}{4}\implies x=10\dfrac{3}{4}$