Basic Math Examples

$2 (\frac{1}{2} y + 1) = - 3 (2 y - 1) + 4 (2 y + 1)$

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.

$- 3 (2 y - 1) + 4 (2 y + 1) = 2 (\frac{1}{2} y + 1)$

Step 2

Simplify $- 3 (2 y - 1) + 4 (2 y + 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 3 (2 y) - 3 \cdot - 1 + 4 (2 y + 1) = 2 (\frac{1}{2} y + 1)$

Step 2.1.2

Multiply $2$ by $- 3$ .

$- 6 y - 3 \cdot - 1 + 4 (2 y + 1) = 2 (\frac{1}{2} y + 1)$

Step 2.1.3

Multiply $- 3$ by $- 1$ .

$- 6 y + 3 + 4 (2 y + 1) = 2 (\frac{1}{2} y + 1)$

Step 2.1.4

Apply the distributive property.

$- 6 y + 3 + 4 (2 y) + 4 \cdot 1 = 2 (\frac{1}{2} y + 1)$

Step 2.1.5

Multiply $2$ by $4$ .

$- 6 y + 3 + 8 y + 4 \cdot 1 = 2 (\frac{1}{2} y + 1)$

Step 2.1.6

Multiply $4$ by $1$ .

$- 6 y + 3 + 8 y + 4 = 2 (\frac{1}{2} y + 1)$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $- 6 y$ and $8 y$ .

$2 y + 3 + 4 = 2 (\frac{1}{2} y + 1)$

Step 2.2.2

Add $3$ and $4$ .

$2 y + 7 = 2 (\frac{1}{2} y + 1)$

Step 3

Simplify $2 (\frac{1}{2} y + 1)$ .

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Step 3.1

Combine $\frac{1}{2}$ and $y$ .

$2 y + 7 = 2 (\frac{y}{2} + 1)$

Step 3.2

Apply the distributive property.

$2 y + 7 = 2 \frac{y}{2} + 2 \cdot 1$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

$2 y + 7 = 2 \frac{y}{2} + 2 \cdot 1$

Step 3.3.2

Rewrite the expression.

$2 y + 7 = y + 2 \cdot 1$

Step 3.4

Multiply $2$ by $1$ .

$2 y + 7 = y + 2$

Step 4

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

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Step 4.1

Subtract $y$ from both sides of the equation.

$2 y + 7 - y = 2$

Step 4.2

Subtract $y$ from $2 y$ .

$y + 7 = 2$

Step 5

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

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Step 5.1

Subtract $7$ from both sides of the equation.

$y = 2 - 7$

Step 5.2

Subtract $7$ from $2$ .

$y = - 5$