Algebra Examples

$\frac{1}{2} b + \frac{9}{4} = \frac{7}{4}$

Step 1

Combine $\frac{1}{2}$ and $b$ .

$\frac{b}{2} + \frac{9}{4} = \frac{7}{4}$

Step 2

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

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Step 2.1

Subtract $\frac{9}{4}$ from both sides of the equation.

$\frac{b}{2} = \frac{7}{4} - \frac{9}{4}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{b}{2} = \frac{7 - 9}{4}$

Step 2.3

Subtract $9$ from $7$ .

$\frac{b}{2} = \frac{- 2}{4}$

Step 2.4

Cancel the common factor of $- 2$ and $4$ .

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Step 2.4.1

Factor $2$ out of $- 2$ .

$\frac{b}{2} = \frac{2 (- 1)}{4}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $4$ .

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

Step 2.4.2.2

Cancel the common factor.

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

Step 2.4.2.3

Rewrite the expression.

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

Step 2.5

Move the negative in front of the fraction.

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

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$b = - 1$