Algebra Examples

$6 (9 y - 1) - 10 (5 y) - 3 y = 22 - 4 (2 y - 12) + 8 (y - 6)$

Step 1

Simplify $6 (9 y - 1) - 10 \cdot (5 y) - 3 y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$6 (9 y) + 6 \cdot - 1 - 10 \cdot (5 y) - 3 y = 22 - 4 (2 y - 12) + 8 (y - 6)$

Step 1.1.2

Multiply $9$ by $6$ .

$54 y + 6 \cdot - 1 - 10 \cdot (5 y) - 3 y = 22 - 4 (2 y - 12) + 8 (y - 6)$

Step 1.1.3

Multiply $6$ by $- 1$ .

$54 y - 6 - 10 \cdot (5 y) - 3 y = 22 - 4 (2 y - 12) + 8 (y - 6)$

Step 1.1.4

Multiply $5$ by $- 10$ .

$54 y - 6 - 50 y - 3 y = 22 - 4 (2 y - 12) + 8 (y - 6)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $50 y$ from $54 y$ .

$4 y - 6 - 3 y = 22 - 4 (2 y - 12) + 8 (y - 6)$

Step 1.2.2

Subtract $3 y$ from $4 y$ .

$y - 6 = 22 - 4 (2 y - 12) + 8 (y - 6)$

Step 2

Simplify $22 - 4 (2 y - 12) + 8 (y - 6)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$y - 6 = 22 - 4 (2 y) - 4 \cdot - 12 + 8 (y - 6)$

Step 2.1.2

Multiply $2$ by $- 4$ .

$y - 6 = 22 - 8 y - 4 \cdot - 12 + 8 (y - 6)$

Step 2.1.3

Multiply $- 4$ by $- 12$ .

$y - 6 = 22 - 8 y + 48 + 8 (y - 6)$

Step 2.1.4

Apply the distributive property.

$y - 6 = 22 - 8 y + 48 + 8 y + 8 \cdot - 6$

Step 2.1.5

Multiply $8$ by $- 6$ .

$y - 6 = 22 - 8 y + 48 + 8 y - 48$

Step 2.2

Combine the opposite terms in $22 - 8 y + 48 + 8 y - 48$ .

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Step 2.2.1

Add $- 8 y$ and $8 y$ .

$y - 6 = 22 + 0 + 48 - 48$

Step 2.2.2

Add $22$ and $0$ .

$y - 6 = 22 + 48 - 48$

Step 2.2.3

Subtract $48$ from $48$ .

$y - 6 = 22 + 0$

Step 2.2.4

Add $22$ and $0$ .

$y - 6 = 22$

Step 3

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

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Step 3.1

Add $6$ to both sides of the equation.

$y = 22 + 6$

Step 3.2

Add $22$ and $6$ .

$y = 28$