Algebra Examples

$4 (y - 3) + 19 = 8 (2 y + 3) + 7$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $8 (2 y + 3)$ from both sides of the equation.

$4 (y - 3) + 19 - 8 (2 y + 3) = 7$

Step 1.2

Subtract $7$ from both sides of the equation.

$4 (y - 3) + 19 - 8 (2 y + 3) - 7 = 0$

Step 2

Simplify $4 (y - 3) + 19 - 8 (2 y + 3) - 7$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$4 y + 4 \cdot - 3 + 19 - 8 (2 y + 3) - 7 = 0$

Step 2.1.2

Multiply $4$ by $- 3$ .

$4 y - 12 + 19 - 8 (2 y + 3) - 7 = 0$

Step 2.1.3

Apply the distributive property.

$4 y - 12 + 19 - 8 (2 y) - 8 \cdot 3 - 7 = 0$

Step 2.1.4

Multiply $2$ by $- 8$ .

$4 y - 12 + 19 - 16 y - 8 \cdot 3 - 7 = 0$

Step 2.1.5

Multiply $- 8$ by $3$ .

$4 y - 12 + 19 - 16 y - 24 - 7 = 0$

Step 2.2

Subtract $16 y$ from $4 y$ .

$- 12 y - 12 + 19 - 24 - 7 = 0$

Step 2.3

Add $- 12$ and $19$ .

$- 12 y + 7 - 24 - 7 = 0$

Step 2.4

Combine the opposite terms in $- 12 y + 7 - 24 - 7$ .

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Step 2.4.1

Subtract $7$ from $7$ .

$- 12 y + 0 - 24 = 0$

Step 2.4.2

Add $- 12 y$ and $0$ .

$- 12 y - 24 = 0$

Step 3

Factor $- 12$ out of $- 12 y - 24$ .

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Step 3.1

Factor $- 12$ out of $- 12 y$ .

$- 12 y - 24 = 0$

Step 3.2

Factor $- 12$ out of $- 24$ .

$- 12 y - 12 \cdot 2 = 0$

Step 3.3

Factor $- 12$ out of $- 12 (y) - 12 (2)$ .

$- 12 (y + 2) = 0$

Step 4

Divide each term in $- 12 (y + 2) = 0$ by $- 12$ and simplify.

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Step 4.1

Divide each term in $- 12 (y + 2) = 0$ by $- 12$ .

$\frac{- 12 (y + 2)}{- 12} = \frac{0}{- 12}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 12$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 12 (y + 2)}{- 12} = \frac{0}{- 12}$

Step 4.2.1.2

Divide $y + 2$ by $1$ .

$y + 2 = \frac{0}{- 12}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $- 12$ .

$y + 2 = 0$

Step 5

Subtract $2$ from both sides of the equation.

$y = - 2$