Pre-Algebra Examples

$11 + 7 b = 1 + 3 b$

Step 1

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

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Step 1.1

Subtract $3 b$ from both sides of the equation.

$11 + 7 b - 3 b = 1$

Step 1.2

Subtract $3 b$ from $7 b$ .

$11 + 4 b = 1$

Step 2

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

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Step 2.1

Subtract $11$ from both sides of the equation.

$4 b = 1 - 11$

Step 2.2

Subtract $11$ from $1$ .

$4 b = - 10$

Step 3

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

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $b$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

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

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Step 3.3.1.1

Factor $2$ out of $- 10$ .

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

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $2$ out of $4$ .

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

Step 3.3.1.2.2

Cancel the common factor.

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

Step 3.3.1.2.3

Rewrite the expression.

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

Step 3.3.2

Move the negative in front of the fraction.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$b = - 2.5$

Mixed Number Form:

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