Linear Algebra Examples

$- 5.7 x + 4 (1 + 5.8 x) = 14 - 3.5 x$

Step 1

Simplify $- 5.7 x + 4 (1 + 5.8 x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 5.7 x + 4 \cdot 1 + 4 (5.8 x) = 14 - 3.5 x$

Step 1.1.2

Multiply $4$ by $1$ .

$- 5.7 x + 4 + 4 (5.8 x) = 14 - 3.5 x$

Step 1.1.3

Multiply $5.8$ by $4$ .

$- 5.7 x + 4 + 23.2 x = 14 - 3.5 x$

Step 1.2

Add $- 5.7 x$ and $23.2 x$ .

$17.5 x + 4 = 14 - 3.5 x$

Step 2

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

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Step 2.1

Add $3.5 x$ to both sides of the equation.

$17.5 x + 4 + 3.5 x = 14$

Step 2.2

Add $17.5 x$ and $3.5 x$ .

$21 x + 4 = 14$

Step 3

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

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Step 3.1

Subtract $4$ from both sides of the equation.

$21 x = 14 - 4$

Step 3.2

Subtract $4$ from $14$ .

$21 x = 10$

Step 4

Divide each term in $21 x = 10$ by $21$ and simplify.

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Step 4.1

Divide each term in $21 x = 10$ by $21$ .

$\frac{21 x}{21} = \frac{10}{21}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $21$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{21 x}{21} = \frac{10}{21}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{10}{21}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $10$ and $21$ .

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Step 4.3.1.1

Rewrite $10$ as $1 (10)$ .

$x = \frac{1 (10)}{21}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Rewrite $21$ as $1 (21)$ .

$x = \frac{1 \cdot 10}{1 \cdot 21}$

Step 4.3.1.2.2

Cancel the common factor.

$x = \frac{1 \cdot 10}{1 \cdot 21}$

Step 4.3.1.2.3

Rewrite the expression.

$x = \frac{10}{21}$

Step 5

The domain is the set of all valid $x$ values.

${x | x = \frac{10}{21}}$

Step 6