Basic Math Examples

$2 a - 1 = 4 (a + 1) + 7 a + 5$

Step 1

Since $a$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 (a + 1) + 7 a + 5 = 2 a - 1$

Step 2

Simplify $4 (a + 1) + 7 a + 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$4 a + 4 \cdot 1 + 7 a + 5 = 2 a - 1$

Step 2.1.2

Multiply $4$ by $1$ .

$4 a + 4 + 7 a + 5 = 2 a - 1$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $4 a$ and $7 a$ .

$11 a + 4 + 5 = 2 a - 1$

Step 2.2.2

Add $4$ and $5$ .

$11 a + 9 = 2 a - 1$

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.

$11 a + 9 - 2 a = - 1$

Step 3.2

Subtract $2 a$ from $11 a$ .

$9 a + 9 = - 1$

Step 4

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

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Step 4.1

Subtract $9$ from both sides of the equation.

$9 a = - 1 - 9$

Step 4.2

Subtract $9$ from $- 1$ .

$9 a = - 10$

Step 5

Divide each term in $9 a = - 10$ by $9$ and simplify.

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Step 5.1

Divide each term in $9 a = - 10$ by $9$ .

$\frac{9 a}{9} = \frac{- 10}{9}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $9$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{9 a}{9} = \frac{- 10}{9}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 10}{9}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$a = - \frac{10}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{10}{9}$

Decimal Form:

$a = - 1.\overline{1}$

Mixed Number Form:

$a = - 1 \frac{1}{9}$