Solve for x |(x+7)/(2x-1)|=2

$| \frac{x + 7}{2 x - 1} | = 2$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$\frac{x + 7}{2 x - 1} = \pm 2$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

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

Find the LCD of the terms in the equation.

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

$2 x - 1, 1$

Remove parentheses.

$2 x - 1, 1$

The LCM of one and any expression is the expression.

$2 x - 1$

Multiply each term in $\frac{x + 7}{2 x - 1} = 2$ by $2 x - 1$ to eliminate the fractions.

Multiply each term in $\frac{x + 7}{2 x - 1} = 2$ by $2 x - 1$ .

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

Simplify the left side.

Cancel the common factor of $2 x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

$x + 7 = 2 (2 x - 1)$

Simplify the right side.

Apply the distributive property.

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

Multiply.

Multiply $2$ by $2$ .

$x + 7 = 4 x + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$x + 7 = 4 x - 2$

Solve the equation.

Move all terms containing $x$ to the left side of the equation.

Subtract $4 x$ from both sides of the equation.

$x + 7 - 4 x = - 2$

Subtract $4 x$ from $x$ .

$- 3 x + 7 = - 2$

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

Subtract $7$ from both sides of the equation.

$- 3 x = - 2 - 7$

Subtract $7$ from $- 2$ .

$- 3 x = - 9$

Divide each term in $- 3 x = - 9$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 9$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 9}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 9}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 9}{- 3}$

Simplify the right side.

Divide $- 9$ by $- 3$ .

$x = 3$

Next, use the negative value of the $\pm$ to find the second solution.

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

Find the LCD of the terms in the equation.

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

$2 x - 1, 1$

Remove parentheses.

$2 x - 1, 1$

The LCM of one and any expression is the expression.

$2 x - 1$

Multiply each term in $\frac{x + 7}{2 x - 1} = - 2$ by $2 x - 1$ to eliminate the fractions.

Multiply each term in $\frac{x + 7}{2 x - 1} = - 2$ by $2 x - 1$ .

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

Simplify the left side.

Cancel the common factor of $2 x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

$x + 7 = - 2 (2 x - 1)$

Simplify the right side.

Apply the distributive property.

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

Multiply.

Multiply $2$ by $- 2$ .

$x + 7 = - 4 x - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$x + 7 = - 4 x + 2$

Solve the equation.

Move all terms containing $x$ to the left side of the equation.

Add $4 x$ to both sides of the equation.

$x + 7 + 4 x = 2$

Add $x$ and $4 x$ .

$5 x + 7 = 2$

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

Subtract $7$ from both sides of the equation.

$5 x = 2 - 7$

Subtract $7$ from $2$ .

$5 x = - 5$

Divide each term in $5 x = - 5$ by $5$ and simplify.

Divide each term in $5 x = - 5$ by $5$ .

$\frac{5 x}{5} = \frac{- 5}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 5}{5}$

Divide $x$ by $1$ .

$x = \frac{- 5}{5}$

Simplify the right side.

Divide $- 5$ by $5$ .

$x = - 1$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 1$

Solve for x |(x+7)/(2x-1)|=2

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