Algebra Examples

$2 (x + 1) + 8 (x - 1) = 5 x$

Step 1

Simplify $2 (x + 1) + 8 (x - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 x + 2 \cdot 1 + 8 (x - 1) = 5 x$

Step 1.1.2

Multiply $2$ by $1$ .

$2 x + 2 + 8 (x - 1) = 5 x$

Step 1.1.3

Apply the distributive property.

$2 x + 2 + 8 x + 8 \cdot - 1 = 5 x$

Step 1.1.4

Multiply $8$ by $- 1$ .

$2 x + 2 + 8 x - 8 = 5 x$

$2 x + 2 + 8 x - 8 = 5 x$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $2 x$ and $8 x$ .

$10 x + 2 - 8 = 5 x$

Step 1.2.2

Subtract $8$ from $2$ .

$10 x - 6 = 5 x$

$10 x - 6 = 5 x$

$10 x - 6 = 5 x$

Step 2

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

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Step 2.1

Subtract $5 x$ from both sides of the equation.

$10 x - 6 - 5 x = 0$

Step 2.2

Subtract $5 x$ from $10 x$ .

$5 x - 6 = 0$

$5 x - 6 = 0$

Step 3

Add $6$ to both sides of the equation.

$5 x = 6$

Step 4

Divide each term in $5 x = 6$ by $5$ and simplify.

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Step 4.1

Divide each term in $5 x = 6$ by $5$ .

$\frac{5 x}{5} = \frac{6}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{6}{5}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{5}$

$x = \frac{6}{5}$

$x = \frac{6}{5}$

$x = \frac{6}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{5}$

Decimal Form:

$x = 1.2$

Mixed Number Form:

$x = 1 \frac{1}{5}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$