Pre-Algebra Examples

$4 y - 5 x = 3 (4 x - 2 y + 1)$

Step 1

Solve for $y$ .

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Step 1.1

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

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Step 1.1.1

Rewrite.

$4 y - 5 x = 0 + 0 + 3 (4 x - 2 y + 1)$

Step 1.1.2

Simplify by adding zeros.

$4 y - 5 x = 3 (4 x - 2 y + 1)$

Step 1.1.3

Apply the distributive property.

$4 y - 5 x = 3 (4 x) + 3 (- 2 y) + 3 \cdot 1$

Step 1.1.4

Simplify.

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Step 1.1.4.1

Multiply $4$ by $3$ .

$4 y - 5 x = 12 x + 3 (- 2 y) + 3 \cdot 1$

Step 1.1.4.2

Multiply $- 2$ by $3$ .

$4 y - 5 x = 12 x - 6 y + 3 \cdot 1$

Step 1.1.4.3

Multiply $3$ by $1$ .

$4 y - 5 x = 12 x - 6 y + 3$

Step 1.2

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

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Step 1.2.1

Add $6 y$ to both sides of the equation.

$4 y - 5 x + 6 y = 12 x + 3$

Step 1.2.2

Add $4 y$ and $6 y$ .

$- 5 x + 10 y = 12 x + 3$

Step 1.3

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

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Step 1.3.1

Add $5 x$ to both sides of the equation.

$10 y = 12 x + 3 + 5 x$

Step 1.3.2

Add $12 x$ and $5 x$ .

$10 y = 17 x + 3$

Step 1.4

Divide each term in $10 y = 17 x + 3$ by $10$ and simplify.

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Step 1.4.1

Divide each term in $10 y = 17 x + 3$ by $10$ .

$\frac{10 y}{10} = \frac{17 x}{10} + \frac{3}{10}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $10$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{10 y}{10} = \frac{17 x}{10} + \frac{3}{10}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{17 x}{10} + \frac{3}{10}$

Step 2

Reorder terms.

$y = \frac{17}{10} x + \frac{3}{10}$

Step 3