Full solution

\frac{2}{7} x+\frac{11}{7} x=\frac{3}{5}

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Given the equation, what is the value of

13 x

Combine like terms: Combine like terms on the left side of the equation. $\newline$ We have $(\frac{2}{7})x + (\frac{11}{7})x$ , which are like terms because they both have the variable $x$ . To combine them, we add their coefficients. $\newline$ $(\frac{2}{7})x + (\frac{11}{7})x = (\frac{2}{7} + \frac{11}{7})x$ $\newline$ = $(\frac{13}{7})x$
Set equal to right side: Set the combined expression equal to the right side of the equation. $\newline$ Now we have $(\frac{13}{7})x = (\frac{3}{5})$ .
Multiply by reciprocal: Solve for $x$ by multiplying both sides of the equation by the reciprocal of $(13/7)$ . To isolate $x$ , we multiply both sides by $7/13$ . $x = (3/5) \times (7/13)$
Calculate value of $13x$ : Perform the multiplication to solve for $x$ . $\newline$ $x = \frac{(3 \times 7)}{(5 \times 13)}$ $\newline$ $x = \frac{21}{65}$
Simplify expression for $13x$ : Calculate the value of $13x$ . To find $13x$ , we multiply $x$ by $13$ . $13x = 13 \times \left(\frac{21}{65}\right)$
Simplify the fraction: Simplify the expression for $13x$ . $\newline$ $13x = \frac{(13 \times 21)}{65}$ $\newline$ $13x = \frac{273}{65}$
Simplify the fraction: Simplify the expression for $13x$ .
$13x = (13 \times 21) / 65$
$13x = 273 / 65$ Simplify the fraction if possible.
$273$ and $65$ have no common factors other than $1$ , so the fraction is already in its simplest form.
$13x = 273 / 65$