Solve for v 3(-0.2v+0.7)+0.3=-0.6(-v+10)

$3 (- 0.2 v + 0.7) + 0.3 = - 0.6 (- v + 10)$

Step 1

Simplify $3 (- 0.2 v + 0.7) + 0.3$ .

Simplify each term.

Apply the distributive property.

$3 (- 0.2 v) + 3 \cdot 0.7 + 0.3 = - 0.6 (- v + 10)$

Multiply $- 0.2$ by $3$ .

$- 0.6 v + 3 \cdot 0.7 + 0.3 = - 0.6 (- v + 10)$

Multiply $3$ by $0.7$ .

$- 0.6 v + 2.1 + 0.3 = - 0.6 (- v + 10)$

Add $2.1$ and $0.3$ .

$- 0.6 v + 2.4 = - 0.6 (- v + 10)$

Step 2

Simplify $- 0.6 (- v + 10)$ .

Apply the distributive property.

$- 0.6 v + 2.4 = - 0.6 (- v) - 0.6 \cdot 10$

Multiply.

Multiply $- 1$ by $- 0.6$ .

$- 0.6 v + 2.4 = 0.6 v - 0.6 \cdot 10$

Multiply $- 0.6$ by $10$ .

$- 0.6 v + 2.4 = 0.6 v - 6$

Step 3

Move all terms containing $v$ to the left side of the equation.

Subtract $0.6 v$ from both sides of the equation.

$- 0.6 v + 2.4 - 0.6 v = - 6$

Subtract $0.6 v$ from $- 0.6 v$ .

$- 1.2 v + 2.4 = - 6$

Step 4

Move all terms not containing $v$ to the right side of the equation.

Subtract $2.4$ from both sides of the equation.

$- 1.2 v = - 6 - 2.4$

Subtract $2.4$ from $- 6$ .

$- 1.2 v = - 8.4$

Step 5

Divide each term in $- 1.2 v = - 8.4$ by $- 1.2$ and simplify.

Divide each term in $- 1.2 v = - 8.4$ by $- 1.2$ .

$\frac{- 1.2 v}{- 1.2} = \frac{- 8.4}{- 1.2}$

Simplify the left side.

Cancel the common factor of $- 1.2$ .

Cancel the common factor.

$\frac{- 1.2 v}{- 1.2} = \frac{- 8.4}{- 1.2}$

Divide $v$ by $1$ .

$v = \frac{- 8.4}{- 1.2}$

Simplify the right side.

Divide $- 8.4$ by $- 1.2$ .

$v = 7$

Solve for v 3(-0.2v+0.7)+0.3=-0.6(-v+10)

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