Solve for r. {:[(4r-6)/(r-7)=(1)/(2)],[r=]:}

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Solve for  r.  {:[(4r-6)/(r-7)=(1)/(2)],[r=]:}

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Clear Fraction by Multiplying: We have the equation (4r - 6) / (r - 7) = 1/2. To solve for r, we need to clear the fraction by multiplying both sides of the equation by the denominator (r - 7). Calculation: (4r - 6) / (r - 7) * (r - 7) = 1/2 * (r - 7) This simplifies to: 4r - 6 = (1/2) * (r - 7)Distribute 1/2 on Right Side: Distribute the 1/2 on the right side of the equation. Calculation: 4r - 6 = (1/2) * r - (1/2) * 7 This simplifies to: 4r - 6 = (1/2) * r - 3.5Move Terms to Isolate r: To isolate r, we need to get all the r terms on one side and the constants on the other. Let's move the (1/2) * r term to the left side by subtracting it from both sides. Calculation: 4r - (1/2) * r - 6 = -3.5 This simplifies to: (8/2) * r - (1/2) * r - 6 = -3.5Combine Like Terms: Combine like terms on the left side of the equation. Calculation: (8/2 - 1/2) * r - 6 = -3.5 This simplifies to: (7/2) * r - 6 = -3.5Add 6 to Both Sides: Add 6 to both sides to isolate the term with r. Calculation: (7/2) * r - 6 + 6 = -3.5 + 6 This simplifies to: (7/2) * r = 2.5Multiply by Reciprocal: Multiply both sides by the reciprocal of (7/2) to solve for r. Calculation: r = 2.5 * (2/7) This simplifies to: r = 5/7

Solve for $r$ . $\newline$ $\begin{array}{l} \frac{4 r-6}{r-7}=\frac{1}{2} \\ r=\square \end{array}$

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Solve for r r r.\newline4r−6r−7=12r=□ \begin{array}{l} \frac{4 r-6}{r-7}=\frac{1}{2} \\ r=\square \end{array} r−74r−6​=21​r=□​

Solve for $r$ . $\newline$ $\begin{array}{l} \frac{4 r-6}{r-7}=\frac{1}{2} \\ r=\square \end{array}$