Pre-Algebra Examples

$10 = \frac{5}{2.25} x + b$

Step 1

Rewrite the equation as $\frac{5}{2.25} x + b = 10$ .

$\frac{5}{2.25} x + b = 10$

Step 2

Divide $5$ by $2.25$ .

$2.\overline{2} x + b = 10$

Step 3

Subtract $b$ from both sides of the equation.

$2.\overline{2} x = 10 - b$

Step 4

Divide each term in $2.\overline{2} x = 10 - b$ by $2.\overline{2}$ and simplify.

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Step 4.1

Divide each term in $2.\overline{2} x = 10 - b$ by $2.\overline{2}$ .

$\frac{2.\overline{2} x}{2.\overline{2}} = \frac{10}{2.\overline{2}} + \frac{- b}{2.\overline{2}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2.\overline{2}$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2.\overline{2} x}{2.\overline{2}} = \frac{10}{2.\overline{2}} + \frac{- b}{2.\overline{2}}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{10}{2.\overline{2}} + \frac{- b}{2.\overline{2}}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Divide $10$ by $2.\overline{2}$ .

$x = 4.5 + \frac{- b}{2.\overline{2}}$

Step 4.3.1.2

Move the negative in front of the fraction.

$x = 4.5 - \frac{b}{2.\overline{2}}$

Step 4.3.1.3

Multiply by $1$ .

$x = 4.5 - \frac{1 b}{2.\overline{2}}$

Step 4.3.1.4

Factor $2.\overline{2}$ out of $2.\overline{2}$ .

$x = 4.5 - \frac{1 b}{2.\overline{2} (1)}$

Step 4.3.1.5

Separate fractions.

$x = 4.5 - (\frac{1}{2.\overline{2}} \cdot \frac{b}{1})$

Step 4.3.1.6

Divide $1$ by $2.\overline{2}$ .

$x = 4.5 - (0.45 \frac{b}{1})$

Step 4.3.1.7

Divide $b$ by $1$ .

$x = 4.5 - (0.45 b)$

Step 4.3.1.8

Multiply $0.45$ by $- 1$ .

$x = 4.5 - 0.45 b$