Algebra Examples

$2 (12 - y) = 23 - (2 y - 1)$

Step 1

Simplify $2 (12 - y)$ .

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Step 1.1

Rewrite.

$0 + 0 + 2 (12 - y) = 23 - (2 y - 1)$

Step 1.2

Simplify by adding zeros.

$2 (12 - y) = 23 - (2 y - 1)$

Step 1.3

Apply the distributive property.

$2 \cdot 12 + 2 (- y) = 23 - (2 y - 1)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $2$ by $12$ .

$24 + 2 (- y) = 23 - (2 y - 1)$

Step 1.4.2

Multiply $- 1$ by $2$ .

$24 - 2 y = 23 - (2 y - 1)$

Step 2

Simplify $23 - (2 y - 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$24 - 2 y = 23 - (2 y) - - 1$

Step 2.1.2

Multiply $2$ by $- 1$ .

$24 - 2 y = 23 - 2 y - - 1$

Step 2.1.3

Multiply $- 1$ by $- 1$ .

$24 - 2 y = 23 - 2 y + 1$

Step 2.2

Add $23$ and $1$ .

$24 - 2 y = - 2 y + 24$

Step 3

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

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Step 3.1

Add $2 y$ to both sides of the equation.

$24 - 2 y + 2 y = 24$

Step 3.2

Combine the opposite terms in $24 - 2 y + 2 y$ .

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Step 3.2.1

Add $- 2 y$ and $2 y$ .

$24 + 0 = 24$

Step 3.2.2

Add $24$ and $0$ .

$24 = 24$

Step 4

Since $24 = 24$ , the equation will always be true for any value of $y$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$