Solve for x 2|x+10|+12=-3|x+10|+62

$2 | x + 10 | + 12 = - 3 | x + 10 | + 62$

Step 1

Move all terms containing $| x + 10 |$ to the left side of the equation.

Add $3 | x + 10 |$ to both sides of the equation.

$2 | x + 10 | + 12 + 3 | x + 10 | = 62$

Add $2 | x + 10 |$ and $3 | x + 10 |$ .

$5 | x + 10 | + 12 = 62$

Step 2

Move all terms not containing $| x + 10 |$ to the right side of the equation.

Subtract $12$ from both sides of the equation.

$5 | x + 10 | = 62 - 12$

Subtract $12$ from $62$ .

$5 | x + 10 | = 50$

Step 3

Divide each term in $5 | x + 10 | = 50$ by $5$ and simplify.

Divide each term in $5 | x + 10 | = 50$ by $5$ .

$\frac{5 | x + 10 |}{5} = \frac{50}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 | x + 10 |}{5} = \frac{50}{5}$

Divide $| x + 10 |$ by $1$ .

$| x + 10 | = \frac{50}{5}$

Simplify the right side.

Divide $50$ by $5$ .

$| x + 10 | = 10$

Step 4

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

$x + 10 = \pm 10$

Step 5

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.

$x + 10 = 10$

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

Subtract $10$ from both sides of the equation.

$x = 10 - 10$

Subtract $10$ from $10$ .

$x = 0$

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

$x + 10 = - 10$

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

Subtract $10$ from both sides of the equation.

$x = - 10 - 10$

Subtract $10$ from $- 10$ .

$x = - 20$

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

$x = 0, - 20$

Step 6

Solve for x 2|x+10|+12=-3|x+10|+62

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