Basic Math Examples

$2 (7 - 3 (1 - y)) + 9 = - 2 + 2 (6 (y + 1) - 3 y)$

Step 1

Since

$y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 2 + 2 (6 (y + 1) - 3 y) = 2 (7 - 3 (1 - y)) + 9$

Step 2

Simplify

$- 2 + 2 (6 (y + 1) - 3 y)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Apply the distributive property.

$- 2 + 2 (6 y + 6 \cdot 1 - 3 y) = 2 (7 - 3 (1 - y)) + 9$

Step 2.1.1.2

Multiply

$6$ by

$1$ .

$- 2 + 2 (6 y + 6 - 3 y) = 2 (7 - 3 (1 - y)) + 9$

Step 2.1.2

Subtract

$3 y$ from

$6 y$ .

$- 2 + 2 (3 y + 6) = 2 (7 - 3 (1 - y)) + 9$

Step 2.1.3

Apply the distributive property.

$- 2 + 2 (3 y) + 2 \cdot 6 = 2 (7 - 3 (1 - y)) + 9$

Step 2.1.4

Multiply

$3$ by

$2$ .

$- 2 + 6 y + 2 \cdot 6 = 2 (7 - 3 (1 - y)) + 9$

Step 2.1.5

Multiply

$2$ by

$6$ .

$- 2 + 6 y + 12 = 2 (7 - 3 (1 - y)) + 9$

Step 2.2

Add

$- 2$ and

$12$ .

$6 y + 10 = 2 (7 - 3 (1 - y)) + 9$

Step 3

Simplify

$2 (7 - 3 (1 - y)) + 9$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Simplify each term.

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Step 3.1.1.1

Apply the distributive property.

$6 y + 10 = 2 (7 - 3 \cdot 1 - 3 (- y)) + 9$

Step 3.1.1.2

Multiply

$- 3$ by

$1$ .

$6 y + 10 = 2 (7 - 3 - 3 (- y)) + 9$

Step 3.1.1.3

Multiply

$- 1$ by

$- 3$ .

$6 y + 10 = 2 (7 - 3 + 3 y) + 9$

Step 3.1.2

Subtract

$3$ from

$7$ .

$6 y + 10 = 2 (4 + 3 y) + 9$

Step 3.1.3

Apply the distributive property.

$6 y + 10 = 2 \cdot 4 + 2 (3 y) + 9$

Step 3.1.4

Multiply

$2$ by

$4$ .

$6 y + 10 = 8 + 2 (3 y) + 9$

Step 3.1.5

Multiply

$3$ by

$2$ .

$6 y + 10 = 8 + 6 y + 9$

Step 3.2

Add

$8$ and

$9$ .

$6 y + 10 = 6 y + 17$

Step 4

Move all terms containing

$y$ to the left side of the equation.

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Step 4.1

Subtract

$6 y$ from both sides of the equation.

$6 y + 10 - 6 y = 17$

Step 4.2

Combine the opposite terms in

$6 y + 10 - 6 y$ .

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Step 4.2.1

Subtract

$6 y$ from

$6 y$ .

$0 + 10 = 17$

Step 4.2.2

Add

$0$ and

$10$ .

$10 = 17$

Step 5

Since

$10 \neq 17$ , there are no solutions.

No solution