Algebra Examples

$3 x + 9 = \frac{7}{2} y$

Step 1

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

Step 2

Multiply both sides by $2$ .

$2 (3 x + 9) = 2 (\frac{7}{2} y)$

Step 3

Simplify the left side.

Tap for more steps...

Step 3.1

Simplify $2 (3 x + 9)$ .

Tap for more steps...

Step 3.1.1

Apply the distributive property.

$2 (3 x) + 2 \cdot 9 = 2 (\frac{7}{2} y)$

Step 3.1.2

Multiply.

Tap for more steps...

Step 3.1.2.1

Multiply $3$ by $2$ .

$6 x + 2 \cdot 9 = 2 (\frac{7}{2} y)$

Step 3.1.2.2

Multiply $2$ by $9$ .

$6 x + 18 = 2 (\frac{7}{2} y)$

Step 4

Simplify the right side.

Tap for more steps...

Step 4.1

Simplify $2 (\frac{7}{2} y)$ .

Tap for more steps...

Step 4.1.1

Combine $\frac{7}{2}$ and $y$ .

$6 x + 18 = 2 \frac{7 y}{2}$

Step 4.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.2.1

Cancel the common factor.

$6 x + 18 = 2 \frac{7 y}{2}$

Step 4.1.2.2

Rewrite the expression.

$6 x + 18 = 7 y$

Step 5

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

Tap for more steps...

Step 5.1

Subtract $7 y$ from both sides of the equation.

$6 x + 18 - 7 y = 0$

Step 5.2

Move $18$ .

$6 x - 7 y + 18 = 0$

Step 6

Subtract $18$ from both sides of the equation.

$6 x - 7 y = - 18$

Step 7