How do you solve and check your solutions to $- 5.3 = 2.2 v - 8.6$ $-5.3=2.2v-8.6$ ?

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Answer 1 · 2017-01-31T22:55:06

See the entire solution and validation process below:

First, add $8.6$ $color(red)(8.6)$ to the equation to isolate the $v$ $v$ term while keeping the equation balanced:

$- 5.3 + 8.6 = 2.2 v - 8.6 + 8.6$ $-5.3 + color(red)(8.6) = 2.2v - 8.6 + color(red)(8.6)$

$3.3 = 2.2 v - 0$ $3.3 = 2.2v - 0$

$3.3 = 2.2 v$ $3.3 = 2.2v$

Now, divide each side of the equation by $2.2$ $color(red)(2.2)$ to solve for $v$ $v$ while keeping the equation balanced:

$\frac{3.3}{2.2} = \frac{2.2 v}{2.2}$ $3.3/color(red)(2.2) = (2.2v)/color(red)(2.2)$

$(3 xx 1.1)/(2 xx 1.1) = (color(red)(cancel(color(black)(2.2)))v)/cancel(color(red)(2.2))$

$(3 xx cancel(1.1))/(2 xx cancel(1.1)) = v$

$3/2 = v$

$v = 3/2$

Now to check the solution substitute $3/2$ for $v$ and calculate the right side of the equation and ensure it is equal $-5.3$

$-5.3 = (2.2 xx 3/2) - 8.6$

$-5.3 = 3.3 - 8.6$

$-5.3 = -5.3$

Because both sides of the equation are equal $v = 3/2$ is a valid solution.

How do you solve and check your solutions to -5.3=2.2v-8.6−5.3=2.2v−8.6-5.3=2.2v-8.6?