Solve for x 4(x-2)+x=1/2(10x-6)

$4 (x - 2) + x = \frac{1}{2} (10 x - 6)$

Simplify $4 (x - 2) + x$ .

Simplify each term.

Apply the distributive property.

$4 x + 4 \cdot - 2 + x = \frac{1}{2} \cdot (10 x - 6)$

Multiply $4$ by $- 2$ .

$4 x - 8 + x = \frac{1}{2} \cdot (10 x - 6)$

Add $4 x$ and $x$ .

$5 x - 8 = \frac{1}{2} \cdot (10 x - 6)$

Simplify $\frac{1}{2} \cdot (10 x - 6)$ .

Apply the distributive property.

$5 x - 8 = \frac{1}{2} (10 x) + \frac{1}{2} \cdot - 6$

Cancel the common factor of $2$ .

Factor $2$ out of $10 x$ .

$5 x - 8 = \frac{1}{2} (2 (5 x)) + \frac{1}{2} \cdot - 6$

Cancel the common factor.

$5 x - 8 = \frac{1}{2} (2 (5 x)) + \frac{1}{2} \cdot - 6$

Rewrite the expression.

$5 x - 8 = 5 x + \frac{1}{2} \cdot - 6$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

$5 x - 8 = 5 x + \frac{1}{2} \cdot (2 (- 3))$

Cancel the common factor.

$5 x - 8 = 5 x + \frac{1}{2} \cdot (2 \cdot - 3)$

Rewrite the expression.

$5 x - 8 = 5 x - 3$

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

Subtract $5 x$ from both sides of the equation.

$5 x - 8 - 5 x = - 3$

Combine the opposite terms in $5 x - 8 - 5 x$ .

Subtract $5 x$ from $5 x$ .

$0 - 8 = - 3$

Subtract $8$ from $0$ .

$- 8 = - 3$

Since $- 8 \neq - 3$ , there are no solutions.

No solution