Pre-Algebra Examples

$\frac{3.01}{\sqrt{4.41}} \cdot (3.561 y - \frac{x}{2.05}) = x$

Step 1

Simplify.

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Step 1.1

Simplify the denominator.

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Step 1.1.1

Rewrite $4.41$ as ${2.1}^{2}$ .

$\frac{3.01}{\sqrt{{2.1}^{2}}} \cdot (3.561 y - \frac{x}{2.05}) = x$

Step 1.1.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{3.01}{2.1} \cdot (3.561 y - \frac{x}{2.05}) = x$

Step 1.2

Divide $3.01$ by $2.1$ .

$1.4\overline{3} \cdot (3.561 y - \frac{x}{2.05}) = x$

Step 2

Divide each term in $1.4\overline{3} \cdot (3.561 y - \frac{x}{2.05}) = x$ by $1.4\overline{3}$ and simplify.

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Step 2.1

Divide each term in $1.4\overline{3} \cdot (3.561 y - \frac{x}{2.05}) = x$ by $1.4\overline{3}$ .

$\frac{1.4\overline{3} \cdot (3.561 y - \frac{x}{2.05})}{1.4\overline{3}} = \frac{x}{1.4\overline{3}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $1.4\overline{3}$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{1.4\overline{3} \cdot (3.561 y - \frac{x}{2.05})}{1.4\overline{3}} = \frac{x}{1.4\overline{3}}$

Step 2.2.1.2

Divide $3.561 y - \frac{x}{2.05}$ by $1$ .

$3.561 y - \frac{x}{2.05} = \frac{x}{1.4\overline{3}}$

Step 2.2.2

Simplify each term.

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Step 2.2.2.1

Multiply by $1$ .

$3.561 y - \frac{1 x}{2.05} = \frac{x}{1.4\overline{3}}$

Step 2.2.2.2

Factor $2.05$ out of $2.05$ .

$3.561 y - \frac{1 x}{2.05 (1)} = \frac{x}{1.4\overline{3}}$

Step 2.2.2.3

Separate fractions.

$3.561 y - (\frac{1}{2.05} \cdot \frac{x}{1}) = \frac{x}{1.4\overline{3}}$

Step 2.2.2.4

Divide $1$ by $2.05$ .

$3.561 y - (0.\overline{48780} \frac{x}{1}) = \frac{x}{1.4\overline{3}}$

Step 2.2.2.5

Divide $x$ by $1$ .

$3.561 y - (0.\overline{48780} x) = \frac{x}{1.4\overline{3}}$

Step 2.2.2.6

Multiply $0.\overline{48780}$ by $- 1$ .

$3.561 y - 0.\overline{48780} x = \frac{x}{1.4\overline{3}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply by $1$ .

$3.561 y - 0.\overline{48780} x = \frac{1 x}{1.4\overline{3}}$

Step 2.3.2

Factor $1.4\overline{3}$ out of $1.4\overline{3}$ .

$3.561 y - 0.\overline{48780} x = \frac{1 x}{1.4\overline{3} (1)}$

Step 2.3.3

Separate fractions.

$3.561 y - 0.\overline{48780} x = \frac{1}{1.4\overline{3}} \cdot \frac{x}{1}$

Step 2.3.4

Divide $1$ by $1.4\overline{3}$ .

$3.561 y - 0.\overline{48780} x = 0.69767441 \frac{x}{1}$

Step 2.3.5

Divide $x$ by $1$ .

$3.561 y - 0.\overline{48780} x = 0.69767441 x$

Step 3

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

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Step 3.1

Add $0.\overline{48780} x$ to both sides of the equation.

$3.561 y = 0.69767441 x + 0.\overline{48780} x$

Step 3.2

Add $0.69767441 x$ and $0.\overline{48780} x$ .

$3.561 y = 1.18547929 x$

Step 4

Divide each term in $3.561 y = 1.18547929 x$ by $3.561$ and simplify.

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Step 4.1

Divide each term in $3.561 y = 1.18547929 x$ by $3.561$ .

$\frac{3.561 y}{3.561} = \frac{1.18547929 x}{3.561}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3.561$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3.561 y}{3.561} = \frac{1.18547929 x}{3.561}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{1.18547929 x}{3.561}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Factor $1.18547929$ out of $1.18547929 x$ .

$y = \frac{1.18547929 (x)}{3.561}$

Step 4.3.2

Factor $3.561$ out of $3.561$ .

$y = \frac{1.18547929 (x)}{3.561 (1)}$

Step 4.3.3

Separate fractions.

$y = \frac{1.18547929}{3.561} \cdot \frac{x}{1}$

Step 4.3.4

Divide $1.18547929$ by $3.561$ .

$y = 0.33290628 \frac{x}{1}$

Step 4.3.5

Divide $x$ by $1$ .

$y = 0.33290628 x$

Step 5

The given equation $y = 0.33290628 x$ can not be written as $y = k x^{2}$ , so $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x$