Pre-Algebra Examples

$5 (a + 10 - (2 a + 1)) = 2 (a - 1) - 4 (2 a + 5)$

Step 1

Simplify $5 (a + 10 - (2 a + 1))$ .

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Step 1.1

Rewrite.

$0 + 0 + 5 (a + 10 - (2 a + 1)) = 2 (a - 1) - 4 (2 a + 5)$

Step 1.2

Simplify by adding zeros.

$5 (a + 10 - (2 a + 1)) = 2 (a - 1) - 4 (2 a + 5)$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$5 (a + 10 - (2 a) - 1 \cdot 1) = 2 (a - 1) - 4 (2 a + 5)$

Step 1.3.2

Multiply $2$ by $- 1$ .

$5 (a + 10 - 2 a - 1 \cdot 1) = 2 (a - 1) - 4 (2 a + 5)$

Step 1.3.3

Multiply $- 1$ by $1$ .

$5 (a + 10 - 2 a - 1) = 2 (a - 1) - 4 (2 a + 5)$

Step 1.4

Simplify terms.

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Step 1.4.1

Subtract $2 a$ from $a$ .

$5 (- a + 10 - 1) = 2 (a - 1) - 4 (2 a + 5)$

Step 1.4.2

Subtract $1$ from $10$ .

$5 (- a + 9) = 2 (a - 1) - 4 (2 a + 5)$

Step 1.4.3

Apply the distributive property.

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

Step 1.4.4

Multiply.

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Step 1.4.4.1

Multiply $- 1$ by $5$ .

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

Step 1.4.4.2

Multiply $5$ by $9$ .

$- 5 a + 45 = 2 (a - 1) - 4 (2 a + 5)$

Step 2

Simplify $2 (a - 1) - 4 (2 a + 5)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 5 a + 45 = 2 a + 2 \cdot - 1 - 4 (2 a + 5)$

Step 2.1.2

Multiply $2$ by $- 1$ .

$- 5 a + 45 = 2 a - 2 - 4 (2 a + 5)$

Step 2.1.3

Apply the distributive property.

$- 5 a + 45 = 2 a - 2 - 4 (2 a) - 4 \cdot 5$

Step 2.1.4

Multiply $2$ by $- 4$ .

$- 5 a + 45 = 2 a - 2 - 8 a - 4 \cdot 5$

Step 2.1.5

Multiply $- 4$ by $5$ .

$- 5 a + 45 = 2 a - 2 - 8 a - 20$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $8 a$ from $2 a$ .

$- 5 a + 45 = - 6 a - 2 - 20$

Step 2.2.2

Subtract $20$ from $- 2$ .

$- 5 a + 45 = - 6 a - 22$

Step 3

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

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Step 3.1

Add $6 a$ to both sides of the equation.

$- 5 a + 45 + 6 a = - 22$

Step 3.2

Add $- 5 a$ and $6 a$ .

$a + 45 = - 22$

Step 4

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

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Step 4.1

Subtract $45$ from both sides of the equation.

$a = - 22 - 45$

Step 4.2

Subtract $45$ from $- 22$ .

$a = - 67$