Pre-Algebra Examples

$y + 3 = \frac{7}{16} \cdot (x + 3)$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Multiply both sides by $16$ .

$16 (y + 3) = 16 (\frac{7}{16} \cdot (x + 3))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $16 (y + 3)$ .

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Step 3.1.1

Apply the distributive property.

$16 y + 16 \cdot 3 = 16 (\frac{7}{16} \cdot (x + 3))$

Step 3.1.2

Multiply $16$ by $3$ .

$16 y + 48 = 16 (\frac{7}{16} \cdot (x + 3))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $16 (\frac{7}{16} \cdot (x + 3))$ .

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Step 4.1.1

Apply the distributive property.

$16 y + 48 = 16 (\frac{7}{16} x + \frac{7}{16} \cdot 3)$

Step 4.1.2

Combine $\frac{7}{16}$ and $x$ .

$16 y + 48 = 16 (\frac{7 x}{16} + \frac{7}{16} \cdot 3)$

Step 4.1.3

Multiply $\frac{7}{16} \cdot 3$ .

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Step 4.1.3.1

Combine $\frac{7}{16}$ and $3$ .

$16 y + 48 = 16 (\frac{7 x}{16} + \frac{7 \cdot 3}{16})$

Step 4.1.3.2

Multiply $7$ by $3$ .

$16 y + 48 = 16 (\frac{7 x}{16} + \frac{21}{16})$

Step 4.1.4

Apply the distributive property.

$16 y + 48 = 16 \frac{7 x}{16} + 16 (\frac{21}{16})$

Step 4.1.5

Cancel the common factor of $16$ .

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Step 4.1.5.1

Cancel the common factor.

$16 y + 48 = 16 \frac{7 x}{16} + 16 (\frac{21}{16})$

Step 4.1.5.2

Rewrite the expression.

$16 y + 48 = 7 x + 16 (\frac{21}{16})$

Step 4.1.6

Cancel the common factor of $16$ .

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Step 4.1.6.1

Cancel the common factor.

$16 y + 48 = 7 x + 16 (\frac{21}{16})$

Step 4.1.6.2

Rewrite the expression.

$16 y + 48 = 7 x + 21$

Step 5

Rewrite the equation.

$7 x + 21 = 16 y + 48$

Step 6

Move all terms containing variables to the left side of the equation.

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Step 6.1

Subtract $16 y$ from both sides of the equation.

$7 x + 21 - 16 y = 48$

Step 6.2

Move $21$ .

$7 x - 16 y + 21 = 48$

Step 7

Move all terms not containing a variable to the right side of the equation.

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Step 7.1

Subtract $21$ from both sides of the equation.

$7 x - 16 y = 48 - 21$

Step 7.2

Subtract $21$ from $48$ .

$7 x - 16 y = 27$

Step 8