Algebra Examples

$3 = \frac{2}{7 + x}$

Step 1

Rewrite the equation as $\frac{2}{7 + x} = 3$ .

$\frac{2}{7 + x} = 3$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$7 + x, 1$

Step 2.2

Remove parentheses.

$7 + x, 1$

Step 2.3

The LCM of one and any expression is the expression.

$7 + x$

Step 3

Multiply each term in $\frac{2}{7 + x} = 3$ by $7 + x$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{2}{7 + x} = 3$ by $7 + x$ .

$\frac{2}{7 + x} (7 + x) = 3 (7 + x)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $7 + x$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2}{7 + x} (7 + x) = 3 (7 + x)$

Step 3.2.1.2

Rewrite the expression.

$2 = 3 (7 + x)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$2 = 3 \cdot 7 + 3 x$

Step 3.3.2

Multiply $3$ by $7$ .

$2 = 21 + 3 x$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $21 + 3 x = 2$ .

$21 + 3 x = 2$

Step 4.2

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

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Step 4.2.1

Subtract $21$ from both sides of the equation.

$3 x = 2 - 21$

Step 4.2.2

Subtract $21$ from $2$ .

$3 x = - 19$

Step 4.3

Divide each term in $3 x = - 19$ by $3$ and simplify.

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Step 4.3.1

Divide each term in $3 x = - 19$ by $3$ .

$\frac{3 x}{3} = \frac{- 19}{3}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $3$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 19}{3}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 19}{3}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Move the negative in front of the fraction.

$x = - \frac{19}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{19}{3}$

Decimal Form:

$x = - 6.\overline{3}$

Mixed Number Form:

$x = - 6 \frac{1}{3}$