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Solving a linear equation with several occurrences of the variable:... Solve for \( v \). \( \quad-3 v+11=-8 v+51 \) Simplify your answer as much as possible. \( v=\square \)

Ask by Harris Henry. in the United States
Jan 22,2025

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Answer

\( v = 8 \)

Solution

To solve the linear equation for \( v \): \[ -3v + 11 = -8v + 51 \] **Step 1: Gather like terms involving \( v \) on one side.** Add \( 8v \) to both sides to move all \( v \)-terms to the left side: \[ -3v + 8v + 11 = 51 \] **Step 2: Combine like terms.** \[ 5v + 11 = 51 \] **Step 3: Isolate the term with \( v \).** Subtract \( 11 \) from both sides: \[ 5v = 40 \] **Step 4: Solve for \( v \).** Divide both sides by \( 5 \): \[ v = \frac{40}{5} = 8 \] **Final Answer:** \[ v = 8 \]

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To solve the equation \(-3v + 11 = -8v + 51\), start by getting all terms involving \(v\) on one side and the constant terms on the other. You can add \(8v\) to both sides to get: \(-3v + 8v + 11 = 51\) This simplifies to: \(5v + 11 = 51\) Next, subtract \(11\) from both sides to isolate the term with \(v\): \(5v = 51 - 11\) This simplifies to: \(5v = 40\) Now, divide both sides by \(5\) to solve for \(v\): \(v = \frac{40}{5} = 8\) So, \(v = 8\). \(v = 8\)

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