Basic Math Examples

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

Step 1

Simplify $3 (y - \frac{2}{3})$ .

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Step 1.1

Rewrite.

$3 y - 2 = 0 + 0 + 3 (y - \frac{2}{3})$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

$3 y - 2 = 3 y - 2$

Step 2

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

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Step 2.1

Subtract $3 y$ from both sides of the equation.

$3 y - 2 - 3 y = - 2$

Step 2.2

Combine the opposite terms in $3 y - 2 - 3 y$ .

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Step 2.2.1

Subtract $3 y$ from $3 y$ .

$0 - 2 = - 2$

Step 2.2.2

Subtract $2$ from $0$ .

$- 2 = - 2$

Step 3

Since $- 2 = - 2$ , the equation will always be true for any value of $y$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$