Algebra Examples

$6 (y + 7) = 3 y$

Step 1

Simplify $6 (y + 7)$ .

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Step 1.1

Rewrite.

$0 + 0 + 6 (y + 7) = 3 y$

Step 1.2

Simplify by adding zeros.

$6 (y + 7) = 3 y$

Step 1.3

Apply the distributive property.

$6 y + 6 \cdot 7 = 3 y$

Step 1.4

Multiply $6$ by $7$ .

$6 y + 42 = 3 y$

Step 2

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

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Step 2.1

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

$6 y + 42 - 3 y = 0$

Step 2.2

Subtract $3 y$ from $6 y$ .

$3 y + 42 = 0$

Step 3

Subtract $42$ from both sides of the equation.

$3 y = - 42$

Step 4

Divide each term in $3 y = - 42$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 y = - 42$ by $3$ .

$\frac{3 y}{3} = \frac{- 42}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 42}{3}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 42}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 42$ by $3$ .

$y = - 14$