Pre-Algebra Examples

$4 (y + 1) - 7 = 3 (y - 1) + Y$

Step 1

Simplify $4 (y + 1) - 7$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 y + 4 \cdot 1 - 7 = 3 (y - 1) + Y$

Step 1.1.2

Multiply $4$ by $1$ .

$4 y + 4 - 7 = 3 (y - 1) + Y$

Step 1.2

Subtract $7$ from $4$ .

$4 y - 3 = 3 (y - 1) + Y$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$4 y - 3 = 3 y + 3 \cdot - 1 + Y$

Step 2.2

Multiply $3$ by $- 1$ .

$4 y - 3 = 3 y - 3 + Y$

Step 3

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

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Step 3.1

Subtract $3 y$ from both sides of the equation.

$4 y - 3 - 3 y = - 3 + Y$

Step 3.2

Subtract $3 y$ from $4 y$ .

$y - 3 = - 3 + Y$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$y = - 3 + Y + 3$

Step 4.2

Combine the opposite terms in $- 3 + Y + 3$ .

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Step 4.2.1

Add $- 3$ and $3$ .

$y = Y + 0$

Step 4.2.2

Add $Y$ and $0$ .

$y = Y$