Solve for x -25=1/2(10x-2)+3x

$- 25 = \frac{1}{2} (10 x - 2) + 3 x$

Rewrite the equation as $\frac{1}{2} \cdot (10 x - 2) + 3 x = - 25$ .

$\frac{1}{2} \cdot (10 x - 2) + 3 x = - 25$

Simplify $\frac{1}{2} \cdot (10 x - 2) + 3 x$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{2} (10 x) + \frac{1}{2} \cdot - 2 + 3 x = - 25$

Cancel the common factor of $2$ .

Factor $2$ out of $10 x$ .

$\frac{1}{2} (2 (5 x)) + \frac{1}{2} \cdot - 2 + 3 x = - 25$

Cancel the common factor.

$\frac{1}{2} (2 (5 x)) + \frac{1}{2} \cdot - 2 + 3 x = - 25$

Rewrite the expression.

$5 x + \frac{1}{2} \cdot - 2 + 3 x = - 25$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$5 x + \frac{1}{2} \cdot (2 (- 1)) + 3 x = - 25$

Cancel the common factor.

$5 x + \frac{1}{2} \cdot (2 \cdot - 1) + 3 x = - 25$

Rewrite the expression.

$5 x - 1 + 3 x = - 25$

Add $5 x$ and $3 x$ .

$8 x - 1 = - 25$

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

Add $1$ to both sides of the equation.

$8 x = - 25 + 1$

Add $- 25$ and $1$ .

$8 x = - 24$

Divide each term in $8 x = - 24$ by $8$ and simplify.

Divide each term in $8 x = - 24$ by $8$ .

$\frac{8 x}{8} = \frac{- 24}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 24}{8}$

Divide $x$ by $1$ .

$x = \frac{- 24}{8}$

Simplify the right side.

Divide $- 24$ by $8$ .

$x = - 3$