Basic Math Examples

$- (5 - (a + 1)) = 9 - (5 - (2 a - 3))$

Step 1

Simplify $- (5 - (a + 1))$ .

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Step 1.1

Rewrite.

$0 + 0 - (5 - (a + 1)) = 9 - (5 - (2 a - 3))$

Step 1.2

Simplify by adding zeros.

$- (5 - (a + 1)) = 9 - (5 - (2 a - 3))$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$- (5 - a - 1 \cdot 1) = 9 - (5 - (2 a - 3))$

Step 1.3.2

Multiply $- 1$ by $1$ .

$- (5 - a - 1) = 9 - (5 - (2 a - 3))$

Step 1.4

Simplify by multiplying through.

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Step 1.4.1

Subtract $1$ from $5$ .

$- (- a + 4) = 9 - (5 - (2 a - 3))$

Step 1.4.2

Apply the distributive property.

$- - a - 1 \cdot 4 = 9 - (5 - (2 a - 3))$

Step 1.5

Multiply $- - a$ .

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Step 1.5.1

Multiply $- 1$ by $- 1$ .

$1 a - 1 \cdot 4 = 9 - (5 - (2 a - 3))$

Step 1.5.2

Multiply $a$ by $1$ .

$a - 1 \cdot 4 = 9 - (5 - (2 a - 3))$

Step 1.6

Multiply $- 1$ by $4$ .

$a - 4 = 9 - (5 - (2 a - 3))$

Step 2

Simplify $9 - (5 - (2 a - 3))$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Apply the distributive property.

$a - 4 = 9 - (5 - (2 a) - - 3)$

Step 2.1.1.2

Multiply $2$ by $- 1$ .

$a - 4 = 9 - (5 - 2 a - - 3)$

Step 2.1.1.3

Multiply $- 1$ by $- 3$ .

$a - 4 = 9 - (5 - 2 a + 3)$

Step 2.1.2

Add $5$ and $3$ .

$a - 4 = 9 - (- 2 a + 8)$

Step 2.1.3

Apply the distributive property.

$a - 4 = 9 - (- 2 a) - 1 \cdot 8$

Step 2.1.4

Multiply $- 2$ by $- 1$ .

$a - 4 = 9 + 2 a - 1 \cdot 8$

Step 2.1.5

Multiply $- 1$ by $8$ .

$a - 4 = 9 + 2 a - 8$

Step 2.2

Subtract $8$ from $9$ .

$a - 4 = 2 a + 1$

Step 3

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

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Step 3.1

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

$a - 4 - 2 a = 1$

Step 3.2

Subtract $2 a$ from $a$ .

$- a - 4 = 1$

Step 4

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

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Step 4.1

Add $4$ to both sides of the equation.

$- a = 1 + 4$

Step 4.2

Add $1$ and $4$ .

$- a = 5$

Step 5

Divide each term in $- a = 5$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- a = 5$ by $- 1$ .

$\frac{- a}{- 1} = \frac{5}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{a}{1} = \frac{5}{- 1}$

Step 5.2.2

Divide $a$ by $1$ .

$a = \frac{5}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $5$ by $- 1$ .

$a = - 5$