Question
How many solutions does this equation have? \[ 20-1-10 v=-8 v-19 \]
Ask by French Lang. in Ecuador
Jan 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation has 1 solution: \( v=19 \).
Solution
Solve the equation \( 20-1-10v=-8v-19 \).
Solve the equation by following steps:
- step0: Solve for \(v\):
\(20-1-10v=-8v-19\)
- step1: Subtract the numbers:
\(19-10v=-8v-19\)
- step2: Move the variable to the left side:
\(19-10v+8v=-19\)
- step3: Add the terms:
\(19-2v=-19\)
- step4: Move the constant to the right side:
\(-2v=-19-19\)
- step5: Subtract the numbers:
\(-2v=-38\)
- step6: Change the signs:
\(2v=38\)
- step7: Divide both sides:
\(\frac{2v}{2}=\frac{38}{2}\)
- step8: Divide the numbers:
\(v=19\)
The equation \(20-1-10v=-8v-19\) has 1 solution, which is \(v=19\).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To find out how many solutions the equation has, let's simplify it step by step. We start with: \[ 20 - 1 - 10v = -8v - 19 \] First, combine the constants on the left side: \[ 19 - 10v = -8v - 19 \] Now, let's isolate the variable \(v\). Adding \(10v\) to both sides gives us: \[ 19 = 2v - 19 \] Next, we add 19 to both sides: \[ 38 = 2v \] Finally, divide by 2: \[ v = 19 \] Since we found one unique solution for \(v\), the final answer is that the equation has exactly one solution.
