Solve for r. {:[(4r)/(5r+6)=(1)/(6)],[r=]:}

Set up the equation: Set up the equation. We are given the equation (4r)/(5r+6) = 1/6. We need to solve for r.Cross-multiply to eliminate the fractions: Cross-multiply to eliminate the fractions. Multiply both sides of the equation by (5r+6)*6 to get rid of the denominators. (4r)/(5r+6) * (5r+6) * 6 = (1/6) * (5r+6) * 6Simplify both sides of the equation: Simplify both sides of the equation. On the left side, (5r+6) cancels out, and on the right side, 6 cancels out with 1/6. 4r * 6 = 5r + 6Distribute the 6 on the left side: Distribute the 6 on the left side. 24r = 5r + 6Subtract 5r from both sides: Subtract 5r from both sides to get all r terms on one side. 24r - 5r = 5r - 5r + 6 19r = 6Divide both sides by 19: Divide both sides by 19 to solve for r. r = 6 / 19

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Solve for
r.

{:[(4r)/(5r+6)=(1)/(6)],[r=]:}

Solve for $r$ . $\newline$ $\begin{array}{l} \frac{4 r}{5 r+6}=\frac{1}{6} \\ r=\square \end{array}$

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Algebra 2

Composition of linear functions: find a value

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Q. Solve for

r

\newline

\begin{array}{l} \frac{4 r}{5 r+6}=\frac{1}{6} \\ r=\square \end{array}

Set up the equation: Set up the equation. $\newline$ We are given the equation $(\frac{4r}{5r+6}) = \frac{1}{6}$ . We need to solve for $r$ .
Cross-multiply to eliminate the fractions: Cross-multiply to eliminate the fractions. $\newline$ Multiply both sides of the equation by $(5r+6)\cdot 6$ to get rid of the denominators. $\newline$ $\frac{4r}{5r+6} \cdot (5r+6) \cdot 6 = \frac{1}{6} \cdot (5r+6) \cdot 6$
Simplify both sides of the equation: Simplify both sides of the equation. $\newline$ On the left side, $(5r+6)$ cancels out, and on the right side, $6$ cancels out with $\frac{1}{6}$ . $\newline$ $4r \times 6 = 5r + 6$
Distribute the $6$ on the left side: Distribute the $6$ on the left side. $24r = 5r + 6$
Subtract $5r$ from both sides: Subtract $5r$ from both sides to get all $r$ terms on one side. $\newline$ $24r - 5r = 5r - 5r + 6$ $\newline$ $19r = 6$
Divide both sides by $19$ : Divide both sides by $19$ to solve for $r$ . $r = \frac{6}{19}$