Linear Algebra Examples

$3 (7 x - 2) = 38 - 2 (5 - 2 x)$

Step 1

Simplify $3 (7 x - 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (7 x - 2) = 38 - 2 (5 - 2 x)$

Step 1.2

Simplify by adding zeros.

$3 (7 x - 2) = 38 - 2 (5 - 2 x)$

Step 1.3

Apply the distributive property.

$3 (7 x) + 3 \cdot - 2 = 38 - 2 (5 - 2 x)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $7$ by $3$ .

$21 x + 3 \cdot - 2 = 38 - 2 (5 - 2 x)$

Step 1.4.2

Multiply $3$ by $- 2$ .

$21 x - 6 = 38 - 2 (5 - 2 x)$

Step 2

Simplify $38 - 2 (5 - 2 x)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$21 x - 6 = 38 - 2 \cdot 5 - 2 (- 2 x)$

Step 2.1.2

Multiply $- 2$ by $5$ .

$21 x - 6 = 38 - 10 - 2 (- 2 x)$

Step 2.1.3

Multiply $- 2$ by $- 2$ .

$21 x - 6 = 38 - 10 + 4 x$

Step 2.2

Subtract $10$ from $38$ .

$21 x - 6 = 28 + 4 x$

Step 3

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

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Step 3.1

Subtract $4 x$ from both sides of the equation.

$21 x - 6 - 4 x = 28$

Step 3.2

Subtract $4 x$ from $21 x$ .

$17 x - 6 = 28$

Step 4

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

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Step 4.1

Add $6$ to both sides of the equation.

$17 x = 28 + 6$

Step 4.2

Add $28$ and $6$ .

$17 x = 34$

Step 5

Divide each term in $17 x = 34$ by $17$ and simplify.

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Step 5.1

Divide each term in $17 x = 34$ by $17$ .

$\frac{17 x}{17} = \frac{34}{17}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $17$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{17 x}{17} = \frac{34}{17}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{34}{17}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $34$ by $17$ .

$x = 2$

Step 6

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

${x | x = 2}$

Step 7