Linear Algebra Examples

$- 6 (4 w - 7) = 25 (2 - w)$

Step 1

Simplify $- 6 (4 w - 7)$ .

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Step 1.1

Rewrite.

$0 + 0 - 6 (4 w - 7) = 25 (2 - w)$

Step 1.2

Simplify by adding zeros.

$- 6 (4 w - 7) = 25 (2 - w)$

Step 1.3

Apply the distributive property.

$- 6 (4 w) - 6 \cdot - 7 = 25 (2 - w)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $4$ by $- 6$ .

$- 24 w - 6 \cdot - 7 = 25 (2 - w)$

Step 1.4.2

Multiply $- 6$ by $- 7$ .

$- 24 w + 42 = 25 (2 - w)$

Step 2

Simplify $25 (2 - w)$ .

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Step 2.1

Apply the distributive property.

$- 24 w + 42 = 25 \cdot 2 + 25 (- w)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $25$ by $2$ .

$- 24 w + 42 = 50 + 25 (- w)$

Step 2.2.2

Multiply $- 1$ by $25$ .

$- 24 w + 42 = 50 - 25 w$

Step 3

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

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Step 3.1

Add $25 w$ to both sides of the equation.

$- 24 w + 42 + 25 w = 50$

Step 3.2

Add $- 24 w$ and $25 w$ .

$w + 42 = 50$

Step 4

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

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Step 4.1

Subtract $42$ from both sides of the equation.

$w = 50 - 42$

Step 4.2

Subtract $42$ from $50$ .

$w = 8$

Step 5

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

${w | w = 8}$

Step 6