Algebra Examples

$3 + 11 x = c x + 2 (4 x - 1) + 5$

Step 1

Rewrite the equation as $c x + 2 (4 x - 1) + 5 = 3 + 11 x$ .

$c x + 2 (4 x - 1) + 5 = 3 + 11 x$

Step 2

Simplify $c x + 2 (4 x - 1) + 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$c x + 2 (4 x) + 2 \cdot - 1 + 5 = 3 + 11 x$

Step 2.1.2

Multiply $4$ by $2$ .

$c x + 8 x + 2 \cdot - 1 + 5 = 3 + 11 x$

Step 2.1.3

Multiply $2$ by $- 1$ .

$c x + 8 x - 2 + 5 = 3 + 11 x$

Step 2.2

Add $- 2$ and $5$ .

$c x + 8 x + 3 = 3 + 11 x$

Step 3

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

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Step 3.1

Subtract $8 x$ from both sides of the equation.

$c x + 3 = 3 + 11 x - 8 x$

Step 3.2

Subtract $3$ from both sides of the equation.

$c x = 3 + 11 x - 8 x - 3$

Step 3.3

Combine the opposite terms in $3 + 11 x - 8 x - 3$ .

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Step 3.3.1

Subtract $3$ from $3$ .

$c x = 11 x - 8 x + 0$

Step 3.3.2

Add $11 x - 8 x$ and $0$ .

$c x = 11 x - 8 x$

Step 3.4

Subtract $8 x$ from $11 x$ .

$c x = 3 x$

Step 4

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

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Step 4.1

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $x$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $c$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $x$ .

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Step 4.3.1.1

Cancel the common factor.

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

Step 4.3.1.2

Divide $3$ by $1$ .

$c = 3$