Solve for x 1/2|3-x|+11=4

$\frac{1}{2} | 3 - x | + 11 = 4$

Combine $\frac{1}{2}$ and $| 3 - x |$ .

$\frac{| 3 - x |}{2} + 11 = 4$

Move all terms not containing $| 3 - x |$ to the right side of the equation.

Subtract $11$ from both sides of the equation.

$\frac{| 3 - x |}{2} = 4 - 11$

Subtract $11$ from $4$ .

$\frac{| 3 - x |}{2} = - 7$

Multiply both sides of the equation by $2$ .

$2 \frac{| 3 - x |}{2} = 2 \cdot - 7$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{| 3 - x |}{2} = 2 \cdot - 7$

Rewrite the expression.

$| 3 - x | = 2 \cdot - 7$

Simplify the right side.

Multiply $2$ by $- 7$ .

$| 3 - x | = - 14$

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

No solution