Solve for x (0.7x-2.1)-(0.5-2x)=0.9(3x-1)+0.1

$(0.7 x - 2.1) - (0.5 - 2 x) = 0.9 (3 x - 1) + 0.1$

Step 1

Simplify $0.7 x - 2.1 - (0.5 - 2 x)$ .

Simplify each term.

Apply the distributive property.

$0.7 x - 2.1 - 1 \cdot 0.5 - (- 2 x) = 0.9 (3 x - 1) + 0.1$

Multiply $- 1$ by $0.5$ .

$0.7 x - 2.1 - 0.5 - (- 2 x) = 0.9 (3 x - 1) + 0.1$

Multiply $- 2$ by $- 1$ .

$0.7 x - 2.1 - 0.5 + 2 x = 0.9 (3 x - 1) + 0.1$

Simplify by adding terms.

Add $0.7 x$ and $2 x$ .

$2.7 x - 2.1 - 0.5 = 0.9 (3 x - 1) + 0.1$

Subtract $0.5$ from $- 2.1$ .

$2.7 x - 2.6 = 0.9 (3 x - 1) + 0.1$

Step 2

Simplify $0.9 (3 x - 1) + 0.1$ .

Simplify each term.

Apply the distributive property.

$2.7 x - 2.6 = 0.9 (3 x) + 0.9 \cdot - 1 + 0.1$

Multiply $3$ by $0.9$ .

$2.7 x - 2.6 = 2.7 x + 0.9 \cdot - 1 + 0.1$

Multiply $0.9$ by $- 1$ .

$2.7 x - 2.6 = 2.7 x - 0.9 + 0.1$

Add $- 0.9$ and $0.1$ .

$2.7 x - 2.6 = 2.7 x - 0.8$

Step 3

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

Subtract $2.7 x$ from both sides of the equation.

$2.7 x - 2.6 - 2.7 x = - 0.8$

Subtract $2.7 x$ from $2.7 x$ .

$0 x - 2.6 = - 0.8$

Multiply $0$ by $x$ .

$0 - 2.6 = - 0.8$

Subtract $2.6$ from $0$ .

$- 2.6 = - 0.8$

Step 4

Since $- 2.6 \neq - 0.8$ , there are no solutions.

No solution