Algebra Examples

$2 x - 5 (1 - 3 x) = 1 - 3 (1 - 2 x)$

Step 1

Simplify $2 x - 5 (1 - 3 x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 x - 5 \cdot 1 - 5 (- 3 x) = 1 - 3 (1 - 2 x)$

Step 1.1.2

Multiply $- 5$ by $1$ .

$2 x - 5 - 5 (- 3 x) = 1 - 3 (1 - 2 x)$

Step 1.1.3

Multiply $- 3$ by $- 5$ .

$2 x - 5 + 15 x = 1 - 3 (1 - 2 x)$

Step 1.2

Add $2 x$ and $15 x$ .

$17 x - 5 = 1 - 3 (1 - 2 x)$

Step 2

Simplify $1 - 3 (1 - 2 x)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$17 x - 5 = 1 - 3 \cdot 1 - 3 (- 2 x)$

Step 2.1.2

Multiply $- 3$ by $1$ .

$17 x - 5 = 1 - 3 - 3 (- 2 x)$

Step 2.1.3

Multiply $- 2$ by $- 3$ .

$17 x - 5 = 1 - 3 + 6 x$

Step 2.2

Subtract $3$ from $1$ .

$17 x - 5 = - 2 + 6 x$

Step 3

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

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Step 3.1

Subtract $6 x$ from both sides of the equation.

$17 x - 5 - 6 x = - 2$

Step 3.2

Subtract $6 x$ from $17 x$ .

$11 x - 5 = - 2$

Step 4

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

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Step 4.1

Add $5$ to both sides of the equation.

$11 x = - 2 + 5$

Step 4.2

Add $- 2$ and $5$ .

$11 x = 3$

Step 5

Divide each term in $11 x = 3$ by $11$ and simplify.

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Step 5.1

Divide each term in $11 x = 3$ by $11$ .

$\frac{11 x}{11} = \frac{3}{11}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $11$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{11 x}{11} = \frac{3}{11}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{11}$

Decimal Form:

$x = 0.\overline{27}$