Pre-Algebra Examples

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

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.

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

Step 2

Simplify $3 y + 4 (y - 3)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Multiply $4$ by $- 3$ .

$3 y + 4 y - 12 = - 4 + y$

Step 2.2

Add $3 y$ and $4 y$ .

$7 y - 12 = - 4 + y$

Step 3

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

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Step 3.1

Subtract $y$ from both sides of the equation.

$7 y - 12 - y = - 4$

Step 3.2

Subtract $y$ from $7 y$ .

$6 y - 12 = - 4$

Step 4

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

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Step 4.1

Add $12$ to both sides of the equation.

$6 y = - 4 + 12$

Step 4.2

Add $- 4$ and $12$ .

$6 y = 8$

Step 5

Divide each term in $6 y = 8$ by $6$ and simplify.

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Step 5.1

Divide each term in $6 y = 8$ by $6$ .

$\frac{6 y}{6} = \frac{8}{6}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $6$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{8}{6}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{8}{6}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $8$ and $6$ .

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Step 5.3.1.1

Factor $2$ out of $8$ .

$y = \frac{2 (4)}{6}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $2$ out of $6$ .

$y = \frac{2 \cdot 4}{2 \cdot 3}$

Step 5.3.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 4}{2 \cdot 3}$

Step 5.3.1.2.3

Rewrite the expression.

$y = \frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{4}{3}$

Decimal Form:

$y = 1.\overline{3}$

Mixed Number Form:

$y = 1 \frac{1}{3}$

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