Solve for x 0.4(2x+0.3)=1/3(6x-7.2)

$0.4 (2 x + 0.3) = \frac{1}{3} (6 x - 7.2)$

Step 1

Simplify $0.4 (2 x + 0.3)$ .

Rewrite.

$0 + 0 + 0.4 (2 x + 0.3) = \frac{1}{3} \cdot (6 x - 7.2)$

Simplify by adding zeros.

$0.4 (2 x + 0.3) = \frac{1}{3} \cdot (6 x - 7.2)$

Apply the distributive property.

$0.4 (2 x) + 0.4 \cdot 0.3 = \frac{1}{3} \cdot (6 x - 7.2)$

Multiply.

Multiply $2$ by $0.4$ .

$0.8 x + 0.4 \cdot 0.3 = \frac{1}{3} \cdot (6 x - 7.2)$

Multiply $0.4$ by $0.3$ .

$0.8 x + 0.12 = \frac{1}{3} \cdot (6 x - 7.2)$

Step 2

Simplify $\frac{1}{3} \cdot (6 x - 7.2)$ .

Apply the distributive property.

$0.8 x + 0.12 = \frac{1}{3} (6 x) + \frac{1}{3} \cdot - 7.2$

Cancel the common factor of $3$ .

Factor $3$ out of $6 x$ .

$0.8 x + 0.12 = \frac{1}{3} (3 (2 x)) + \frac{1}{3} \cdot - 7.2$

Cancel the common factor.

$0.8 x + 0.12 = \frac{1}{3} (3 (2 x)) + \frac{1}{3} \cdot - 7.2$

Rewrite the expression.

$0.8 x + 0.12 = 2 x + \frac{1}{3} \cdot - 7.2$

Combine $\frac{1}{3}$ and $- 7.2$ .

$0.8 x + 0.12 = 2 x + \frac{- 7.2}{3}$

Divide $- 7.2$ by $3$ .

$0.8 x + 0.12 = 2 x - 2.4$

Step 3

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

Subtract $2 x$ from both sides of the equation.

$0.8 x + 0.12 - 2 x = - 2.4$

Subtract $2 x$ from $0.8 x$ .

$- 1.2 x + 0.12 = - 2.4$

Step 4

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

Subtract $0.12$ from both sides of the equation.

$- 1.2 x = - 2.4 - 0.12$

Subtract $0.12$ from $- 2.4$ .

$- 1.2 x = - 2.52$

Step 5

Divide each term in $- 1.2 x = - 2.52$ by $- 1.2$ and simplify.

Divide each term in $- 1.2 x = - 2.52$ by $- 1.2$ .

$\frac{- 1.2 x}{- 1.2} = \frac{- 2.52}{- 1.2}$

Simplify the left side.

Cancel the common factor of $- 1.2$ .

Cancel the common factor.

$\frac{- 1.2 x}{- 1.2} = \frac{- 2.52}{- 1.2}$

Divide $x$ by $1$ .

$x = \frac{- 2.52}{- 1.2}$

Simplify the right side.

Divide $- 2.52$ by $- 1.2$ .

$x = 2.1$

Solve for x 0.4(2x+0.3)=1/3(6x-7.2)

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