Solve for v: 2(4v - 5) = 70. Simplify your answer as much as possible.
Understand the Problem
The question asks to solve the algebraic equation 2(4v - 5) = 70 for the variable 'v'. We need to isolate 'v' by performing algebraic operations on both sides of the equation to find its value, simplifying as much as possible.
Answer
$v = 10$
Answer for screen readers
$v = 10$
Steps to Solve
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Distribute the 2 Distribute the 2 on the left side of the equation to both terms inside the parentheses. $2(4v - 5) = 70$ becomes $8v - 10 = 70$.
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Add 10 to both sides Add 10 to both sides of the equation to isolate the term with 'v'. $8v - 10 + 10 = 70 + 10$, which simplifies to $8v = 80$.
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Divide by 8 Divide both sides of the equation by 8 to solve for 'v'. $\frac{8v}{8} = \frac{80}{8}$, which simplifies to $v = 10$.
$v = 10$
More Information
The value of $v$ that satisfies the equation $2(4v - 5) = 70$ is 10.
Tips
A common mistake is forgetting to distribute the 2 to both terms inside the parentheses. For example, some might incorrectly write $8v - 5 = 70$ instead of $8v - 10 = 70$. Another mistake is performing operations on only one side of the equation, thus messing up the equality.
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