Solve for $v$.
$-\frac{1}{2}=\frac{4}{3} v-\frac{9}{5}$
Simplify your answer as much as possible.
$v=$
Answer (2)
Add 5 9 to both sides: − 2 1 + 5 9 = 3 4 v .
Simplify the left side: 10 13 = 3 4 v .
Multiply both sides by 4 3 : 4 3 ⋅ 10 13 = v .
Simplify to find the value of v : v = 40 39 .
Explanation
Problem Setup We are given the equation − 2 1 = 3 4 v − 5 9 and we want to solve for v .
Isolating the Variable Term First, we add 5 9 to both sides of the equation to isolate the term with v on one side: − 2 1 + 5 9 = 3 4 v − 5 9 + 5 9 ⇒ − 2 1 + 5 9 = 3 4 v
Simplifying the Equation Next, we simplify the left side of the equation by finding a common denominator, which is 10: − 10 5 + 10 18 = 3 4 v ⇒ 10 13 = 3 4 v
Solving for v Now, we multiply both sides of the equation by 4 3 to solve for v : 4 3 ⋅ 10 13 = 4 3 ⋅ 3 4 v ⇒ 40 39 = v
Final Answer Therefore, the solution is v = 40 39 .
Examples
Imagine you're adjusting a recipe. You know the final amount you want, and you know how much of one ingredient you've already added. This problem is like figuring out how much more of another ingredient you need to add to reach the desired final amount. Solving linear equations like this helps in many real-life situations, such as adjusting quantities in recipes, calculating distances, or managing budgets.
To solve the equation − 2 1 = 3 4 v − 5 9 for v , first isolate the term with v by adding 5 9 to both sides, yielding 10 13 = 3 4 v . Then multiply both sides by 4 3 to find that v = 40 39 .
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