Algebra Examples

$a - 3 b - 1$ $2 a + 3 b = 16$

Step 1

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

$2 a = 16 - 3 b$

Step 2

Divide each term in $2 a = 16 - 3 b$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 a = 16 - 3 b$ by $2$ .

$\frac{2 a}{2} = \frac{16}{2} + \frac{- 3 b}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{16}{2} + \frac{- 3 b}{2}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a = \frac{16}{2} + \frac{- 3 b}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $16$ by $2$ .

$a = 8 + \frac{- 3 b}{2}$

Step 2.3.1.2

Move the negative in front of the fraction.

$a = 8 - \frac{3 b}{2}$

Step 3

Replace the variable $a$ with $8 - \frac{3 b}{2}$ in the expression.

$(8 - \frac{3 b}{2}) - 3 b - 1$

Step 4

Subtract $1$ from $8$ .

$(- \frac{3 b}{2}) - 3 b + 7$

Step 5

To write $- 3 b$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 b}{2} - 3 b \cdot \frac{2}{2} + 7$

Step 6

Simplify terms.

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Step 6.1

Combine $- 3 b$ and $\frac{2}{2}$ .

$- \frac{3 b}{2} + \frac{- 3 b \cdot 2}{2} + 7$

Step 6.2

Combine the numerators over the common denominator.

$\frac{- 3 b - 3 b \cdot 2}{2} + 7$

Step 7

Simplify each term.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Factor $3 b$ out of $- 3 b - 3 b \cdot 2$ .

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Step 7.1.1.1

Factor $3 b$ out of $- 3 b$ .

$\frac{3 b (- 1) - 3 b \cdot 2}{2} + 7$

Step 7.1.1.2

Factor $3 b$ out of $- 3 b \cdot 2$ .

$\frac{3 b (- 1) + 3 b (- 1 \cdot 2)}{2} + 7$

Step 7.1.1.3

Factor $3 b$ out of $3 b (- 1) + 3 b (- 1 \cdot 2)$ .

$\frac{3 b (- 1 - 1 \cdot 2)}{2} + 7$

Step 7.1.2

Multiply $- 1$ by $2$ .

$\frac{3 b (- 1 - 2)}{2} + 7$

Step 7.1.3

Subtract $2$ from $- 1$ .

$\frac{3 b \cdot - 3}{2} + 7$

Step 7.1.4

Multiply $- 3$ by $3$ .

$\frac{- 9 b}{2} + 7$

Step 7.2

Move the negative in front of the fraction.

$- \frac{9 b}{2} + 7$