Algebra Examples

$6.2 \div (2 x + 1) = 2 \frac{1}{3} \div 4$

Step 1

Simplify the left side.

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Step 1.1

Rewrite the division as a fraction.

$\frac{6.2}{2 x + 1} = 2 \frac{1}{3} \div 4$

Step 2

Simplify the right side.

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Step 2.1

Simplify $2 \frac{1}{3} \div 4$ .

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Step 2.1.1

Convert $2 \frac{1}{3}$ to an improper fraction.

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Step 2.1.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{6.2}{2 x + 1} = (2 + \frac{1}{3}) \div 4$

Step 2.1.1.2

Add $2$ and $\frac{1}{3}$ .

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Step 2.1.1.2.1

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

$\frac{6.2}{2 x + 1} = (2 \cdot \frac{3}{3} + \frac{1}{3}) \div 4$

Step 2.1.1.2.2

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

$\frac{6.2}{2 x + 1} = (\frac{2 \cdot 3}{3} + \frac{1}{3}) \div 4$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$\frac{6.2}{2 x + 1} = \frac{2 \cdot 3 + 1}{3} \div 4$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $2$ by $3$ .

$\frac{6.2}{2 x + 1} = \frac{6 + 1}{3} \div 4$

Step 2.1.1.2.4.2

Add $6$ and $1$ .

$\frac{6.2}{2 x + 1} = \frac{7}{3} \div 4$

Step 2.1.2

Rewrite the division as a fraction.

$\frac{6.2}{2 x + 1} = \frac{\frac{7}{3}}{4}$

Step 2.1.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{6.2}{2 x + 1} = \frac{7}{3} \cdot \frac{1}{4}$

Step 2.1.4

Multiply $\frac{7}{3} \cdot \frac{1}{4}$ .

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Step 2.1.4.1

Multiply $\frac{7}{3}$ by $\frac{1}{4}$ .

$\frac{6.2}{2 x + 1} = \frac{7}{3 \cdot 4}$

Step 2.1.4.2

Multiply $3$ by $4$ .

$\frac{6.2}{2 x + 1} = \frac{7}{12}$

Step 3

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$6.2 \cdot 12 = (2 x + 1) \cdot 7$

Step 4

Solve the equation for $x$ .

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Step 4.1

Rewrite the equation as $(2 x + 1) \cdot 7 = 6.2 \cdot 12$ .

$(2 x + 1) \cdot 7 = 6.2 \cdot 12$

Step 4.2

Multiply $6.2$ by $12$ .

$(2 x + 1) \cdot 7 = 74.4$

Step 4.3

Divide each term in $(2 x + 1) \cdot 7 = 74.4$ by $7$ and simplify.

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Step 4.3.1

Divide each term in $(2 x + 1) \cdot 7 = 74.4$ by $7$ .

$\frac{(2 x + 1) \cdot 7}{7} = \frac{74.4}{7}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $7$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{(2 x + 1) \cdot 7}{7} = \frac{74.4}{7}$

Step 4.3.2.1.2

Divide $2 x + 1$ by $1$ .

$2 x + 1 = \frac{74.4}{7}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $74.4$ by $7$ .

$2 x + 1 = 10.6\overline{285714}$

Step 4.4

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

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Step 4.4.1

Subtract $1$ from both sides of the equation.

$2 x = 10.6\overline{285714} - 1$

Step 4.4.2

Subtract $1$ from $10.6\overline{285714}$ .

$2 x = 9.6\overline{285714}$

Step 4.5

Divide each term in $2 x = 9.6\overline{285714}$ by $2$ and simplify.

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Step 4.5.1

Divide each term in $2 x = 9.6\overline{285714}$ by $2$ .

$\frac{2 x}{2} = \frac{9.6\overline{285714}}{2}$

Step 4.5.2

Simplify the left side.

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Step 4.5.2.1

Cancel the common factor of $2$ .

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Step 4.5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{9.6\overline{285714}}{2}$

Step 4.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{9.6\overline{285714}}{2}$

Step 4.5.3

Simplify the right side.

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Step 4.5.3.1

Divide $9.6\overline{285714}$ by $2$ .

$x = 4.8\overline{142857}$