Algebra Examples

$8 - (2 a + 7) = a + 40$

Step 1

Simplify $8 - (2 a + 7)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$8 - (2 a) - 1 \cdot 7 = a + 40$

Step 1.1.2

Multiply $2$ by $- 1$ .

$8 - 2 a - 1 \cdot 7 = a + 40$

Step 1.1.3

Multiply $- 1$ by $7$ .

$8 - 2 a - 7 = a + 40$

Step 1.2

Subtract $7$ from $8$ .

$- 2 a + 1 = a + 40$

Step 2

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

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Step 2.1

Subtract $a$ from both sides of the equation.

$- 2 a + 1 - a = 40$

Step 2.2

Subtract $a$ from $- 2 a$ .

$- 3 a + 1 = 40$

Step 3

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

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Step 3.1

Subtract $1$ from both sides of the equation.

$- 3 a = 40 - 1$

Step 3.2

Subtract $1$ from $40$ .

$- 3 a = 39$

Step 4

Divide each term in $- 3 a = 39$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 a = 39$ by $- 3$ .

$\frac{- 3 a}{- 3} = \frac{39}{- 3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 3 a}{- 3} = \frac{39}{- 3}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{39}{- 3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $39$ by $- 3$ .

$a = - 13$