Solve for x 15(x-1)=-5(3-x)+10x

$15 (x - 1) = - 5 (3 - x) + 10 x$

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 5 (3 - x) + 10 x = 15 (x - 1)$

Simplify $- 5 (3 - x) + 10 x$ .

Simplify each term.

Apply the distributive property.

$- 5 \cdot 3 - 5 (- x) + 10 x = 15 (x - 1)$

Multiply $- 5$ by $3$ .

$- 15 - 5 (- x) + 10 x = 15 (x - 1)$

Multiply $- 1$ by $- 5$ .

$- 15 + 5 x + 10 x = 15 (x - 1)$

Add $5 x$ and $10 x$ .

$- 15 + 15 x = 15 (x - 1)$

Simplify $15 (x - 1)$ .

Apply the distributive property.

$- 15 + 15 x = 15 x + 15 \cdot - 1$

Multiply $15$ by $- 1$ .

$- 15 + 15 x = 15 x - 15$

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

Subtract $15 x$ from both sides of the equation.

$- 15 + 15 x - 15 x = - 15$

Combine the opposite terms in $- 15 + 15 x - 15 x$ .

Subtract $15 x$ from $15 x$ .

$- 15 + 0 = - 15$

Add $- 15$ and $0$ .

$- 15 = - 15$

Since $- 15 = - 15$ , the equation will always be true for any value of $x$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$