Solve for x 7|x-2|+7=-2|x-2|+2

$7 | x - 2 | + 7 = - 2 | x - 2 | + 2$

Step 1

Move all terms containing $| x - 2 |$ to the left side of the equation.

Add $2 | x - 2 |$ to both sides of the equation.

$7 | x - 2 | + 7 + 2 | x - 2 | = 2$

Add $7 | x - 2 |$ and $2 | x - 2 |$ .

$9 | x - 2 | + 7 = 2$

Step 2

Move all terms not containing $| x - 2 |$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$9 | x - 2 | = 2 - 7$

Subtract $7$ from $2$ .

$9 | x - 2 | = - 5$

Step 3

Divide each term in $9 | x - 2 | = - 5$ by $9$ and simplify.

Divide each term in $9 | x - 2 | = - 5$ by $9$ .

$\frac{9 | x - 2 |}{9} = \frac{- 5}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 | x - 2 |}{9} = \frac{- 5}{9}$

Divide $| x - 2 |$ by $1$ .

$| x - 2 | = \frac{- 5}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$| x - 2 | = - \frac{5}{9}$

Step 4

There is no value of $x$ that makes the equation be true since an absolute value can never be negative.

No solution