Solve for v 3(1.4v-1)=0.2v+1

$3 (1.4 v - 1) = 0.2 v + 1$

Step 1

Simplify $3 (1.4 v - 1)$ .

Rewrite.

$0 + 0 + 3 (1.4 v - 1) = 0.2 v + 1$

Simplify by adding zeros.

$3 (1.4 v - 1) = 0.2 v + 1$

Apply the distributive property.

$3 (1.4 v) + 3 \cdot - 1 = 0.2 v + 1$

Multiply.

Multiply $1.4$ by $3$ .

$4.2 v + 3 \cdot - 1 = 0.2 v + 1$

Multiply $3$ by $- 1$ .

$4.2 v - 3 = 0.2 v + 1$

Step 2

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

Subtract $0.2 v$ from both sides of the equation.

$4.2 v - 3 - 0.2 v = 1$

Subtract $0.2 v$ from $4.2 v$ .

$4 v - 3 = 1$

Step 3

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

Add $3$ to both sides of the equation.

$4 v = 1 + 3$

Add $1$ and $3$ .

$4 v = 4$

Step 4

Divide each term in $4 v = 4$ by $4$ and simplify.

Divide each term in $4 v = 4$ by $4$ .

$\frac{4 v}{4} = \frac{4}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 v}{4} = \frac{4}{4}$

Divide $v$ by $1$ .

$v = \frac{4}{4}$

Simplify the right side.

Divide $4$ by $4$ .

$v = 1$