Basic Math Examples

$3 (y - 2) = 6 (y - 1) - 3 y$

Step 1

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$6 (y - 1) - 3 y = 3 (y - 2)$

Step 2

Simplify $6 (y - 1) - 3 y$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$6 y + 6 \cdot - 1 - 3 y = 3 (y - 2)$

Step 2.1.2

Multiply $6$ by $- 1$ .

$6 y - 6 - 3 y = 3 (y - 2)$

Step 2.2

Subtract $3 y$ from $6 y$ .

$3 y - 6 = 3 (y - 2)$

Step 3

Simplify $3 (y - 2)$ .

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Step 3.1

Apply the distributive property.

$3 y - 6 = 3 y + 3 \cdot - 2$

Step 3.2

Multiply $3$ by $- 2$ .

$3 y - 6 = 3 y - 6$

Step 4

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

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Step 4.1

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

$3 y - 6 - 3 y = - 6$

Step 4.2

Combine the opposite terms in $3 y - 6 - 3 y$ .

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Step 4.2.1

Subtract $3 y$ from $3 y$ .

$0 - 6 = - 6$

Step 4.2.2

Subtract $6$ from $0$ .

$- 6 = - 6$

Step 5

Since $- 6 = - 6$ , the equation will always be true for any value of $y$ .

All real numbers

Step 6

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$