Solve the Absolute Value Inequality for x |x+5|=3x-7

$| x + 5 | = 3 x - 7$

Step 1

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

$x + 5 = \pm (3 x - 7)$

Step 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.

$x + 5 = 3 x - 7$

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

Subtract $3 x$ from both sides of the equation.

$x + 5 - 3 x = - 7$

Subtract $3 x$ from $x$ .

$- 2 x + 5 = - 7$

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

Subtract $5$ from both sides of the equation.

$- 2 x = - 7 - 5$

Subtract $5$ from $- 7$ .

$- 2 x = - 12$

Divide each term in $- 2 x = - 12$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 12$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 12}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 2}$

Simplify the right side.

Divide $- 12$ by $- 2$ .

$x = 6$

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

$x + 5 = - (3 x - 7)$

Simplify $- (3 x - 7)$ .

Rewrite.

$x + 5 = 0 + 0 - (3 x - 7)$

Simplify by adding zeros.

$x + 5 = - (3 x - 7)$

Apply the distributive property.

$x + 5 = - (3 x) - - 7$

Multiply.

Multiply $3$ by $- 1$ .

$x + 5 = - 3 x - - 7$

Multiply $- 1$ by $- 7$ .

$x + 5 = - 3 x + 7$

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

Add $3 x$ to both sides of the equation.

$x + 5 + 3 x = 7$

Add $x$ and $3 x$ .

$4 x + 5 = 7$

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

Subtract $5$ from both sides of the equation.

$4 x = 7 - 5$

Subtract $5$ from $7$ .

$4 x = 2$

Divide each term in $4 x = 2$ by $4$ and simplify.

Divide each term in $4 x = 2$ by $4$ .

$\frac{4 x}{4} = \frac{2}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{2}{4}$

Divide $x$ by $1$ .

$x = \frac{2}{4}$

Simplify the right side.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{2}$

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

$x = 6, \frac{1}{2}$

Step 3

Exclude the solutions that do not make $| x + 5 | = 3 x - 7$ true.

$x = 6$

Solve the Absolute Value Inequality for x |x+5|=3x-7

Related Questions

Support LCMGCF.com by disabling your adblocker.