Pre-Algebra Examples

$1.5 x = y$

Step 1

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

Step 2

Change $1.5$ into a fraction.

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Step 2.1

Multiply by $\frac{10}{10}$ to remove the decimal.

$\frac{10 \cdot 1.5}{10} x = y$

Step 2.2

Multiply $10$ by $1.5$ .

$\frac{15}{10} x = y$

Step 2.3

Cancel the common factor of $15$ and $10$ .

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Step 2.3.1

Factor $5$ out of $15$ .

$\frac{5 (3)}{10} x = y$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $5$ out of $10$ .

$\frac{5 \cdot 3}{5 \cdot 2} x = y$

Step 2.3.2.2

Cancel the common factor.

$\frac{5 \cdot 3}{5 \cdot 2} x = y$

Step 2.3.2.3

Rewrite the expression.

$\frac{3}{2} x = y$

Step 3

Multiply both sides by $2$ .

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

Step 4

Simplify the left side.

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Step 4.1

Simplify $2 (\frac{3}{2} x)$ .

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Step 4.1.1

Combine $\frac{3}{2}$ and $x$ .

$2 \frac{3 x}{2} = 2 y$

Step 4.1.2

Cancel the common factor of $2$ .

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Step 4.1.2.1

Cancel the common factor.

$2 \frac{3 x}{2} = 2 y$

Step 4.1.2.2

Rewrite the expression.

$3 x = 2 y$

Step 5

Subtract $2 y$ from both sides of the equation.

$3 x - 2 y = 0$

Step 6