Algebra Examples

$- 5 y - 9 = - (y - 1)$

Step 1

Simplify $- (y - 1)$ .

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Step 1.1

Rewrite.

$- 5 y - 9 = 0 + 0 - (y - 1)$

Step 1.2

Simplify by adding zeros.

$- 5 y - 9 = - (y - 1)$

Step 1.3

Apply the distributive property.

$- 5 y - 9 = - y - - 1$

Step 1.4

Multiply $- 1$ by $- 1$ .

$- 5 y - 9 = - y + 1$

Step 2

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

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Step 2.1

Add $y$ to both sides of the equation.

$- 5 y - 9 + y = 1$

Step 2.2

Add $- 5 y$ and $y$ .

$- 4 y - 9 = 1$

Step 3

Move all terms not containing $y$ to the right side of the equation.

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Step 3.1

Add $9$ to both sides of the equation.

$- 4 y = 1 + 9$

Step 3.2

Add $1$ and $9$ .

$- 4 y = 10$

Step 4

Divide each term in $- 4 y = 10$ by $- 4$ and simplify.

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Step 4.1

Divide each term in $- 4 y = 10$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{10}{- 4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{10}{- 4}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{10}{- 4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $10$ and $- 4$ .

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Step 4.3.1.1

Factor $2$ out of $10$ .

$y = \frac{2 (5)}{- 4}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $2$ out of $- 4$ .

$y = \frac{2 \cdot 5}{2 \cdot - 2}$

Step 4.3.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 5}{2 \cdot - 2}$

Step 4.3.1.2.3

Rewrite the expression.

$y = \frac{5}{- 2}$

Step 4.3.2

Move the negative in front of the fraction.

$y = - \frac{5}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{5}{2}$

Decimal Form:

$y = - 2.5$

Mixed Number Form:

$y = - 2 \frac{1}{2}$