Question

solve the following linear equation and simplify your answer.
$5v + 10 = -5(-v - 2)$
answer 2 points
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\\(\bigcirc\\) one solution \\(v = \\)
\\(\bigcirc\\) no solution
\\(\bigcirc\\) all real numbers

Explanation:

Step1: Expand the right side

First, we expand the right - hand side of the equation \(5v + 10=-5(-v - 2)\) using the distributive property \(a(b + c)=ab+ac\). Here, \(a=-5\), \(b=-v\) and \(c = - 2\). So, \(-5(-v-2)=(-5)\times(-v)+(-5)\times(-2)=5v + 10\).
The equation becomes \(5v+10 = 5v + 10\).

Step2: Analyze the equation

Subtract \(5v\) from both sides of the equation \(5v+10 = 5v + 10\). We get \((5v - 5v)+10=(5v - 5v)+10\), which simplifies to \(10 = 10\).
This is a true statement for all values of \(v\).

Answer:

All Real Numbers