Question

Solve each equation. 2 1/3(2x-3)=2 1/3

Answer 1

Answer: x = 2

Explanation:

Multiply each term between the parentheses by 2 1/3.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2(1)/(3)(2x-3)=2(1)/(3) \iff \ 2(1)/(3)*2x+2(1)/(3)*(-3)=2(1)/(3) } \end{gathered}$} }`

We calculate the expression of the multiplication.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2(1)/(3)*2x+2(1)/(3)*(-3)=2(1)/(3) \iff \ (14x)/(3)+2(1)/(3)*(-3)=2(1)/(3) } \end{gathered}$} }`

We calculate the multiplication and division of rational numbers.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(14x)/(3)+2(1)/(3)*(-3)=2(1)/(3) \iff (14x)/(3)-7=2(1)/(3) } \end{gathered}$} }`

We convert the mixed fraction to improper.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(14x)/(3)-7=2(1)/(3) \iff (14x)/(3)-7=(7)/(3) } \end{gathered}$} }`

We eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(14x)/(3)-7=(7)/(3) \iff \ 14x-21=7} \end{gathered}$} }`

We move the constant to the right side and change the direction of the sign.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x-21=7 \iff 14x=7+21=28, and \ remains \ 14x=28} \end{gathered}$} }`

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x=28 \iff \ we \ divided \ x=(28)/(14)=x; \Rightarrow x=2. } \end{gathered}$} }`