Algebra Examples

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

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Multiply $- 1$ by $0.5$ .

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

Step 1.1.3

Multiply $- 2$ by $- 1$ .

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

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $0.7 x$ and $2 x$ .

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

Step 1.2.2

Subtract $0.5$ from $- 2.1$ .

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Multiply $3$ by $0.9$ .

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

Step 2.1.3

Multiply $0.9$ by $- 1$ .

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

Step 2.2

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.

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Step 3.1

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

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

Step 3.2

Subtract $2.7 x$ from $2.7 x$ .

$0 x - 2.6 = - 0.8$

Step 3.3

Multiply $0$ by $x$ .

$0 - 2.6 = - 0.8$

Step 3.4

Subtract $2.6$ from $0$ .

$- 2.6 = - 0.8$

Step 4

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

No solution