Solve for x 3(x-5)=2(x-5)+x

$3 (x - 5) = 2 (x - 5) + x$

Step 1

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

$2 (x - 5) + x = 3 (x - 5)$

Step 2

Simplify $2 (x - 5) + x$ .

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot - 5 + x = 3 (x - 5)$

Multiply $2$ by $- 5$ .

$2 x - 10 + x = 3 (x - 5)$

Add $2 x$ and $x$ .

$3 x - 10 = 3 (x - 5)$

Step 3

Simplify $3 (x - 5)$ .

Apply the distributive property.

$3 x - 10 = 3 x + 3 \cdot - 5$

Multiply $3$ by $- 5$ .

$3 x - 10 = 3 x - 15$

Step 4

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

Subtract $3 x$ from both sides of the equation.

$3 x - 10 - 3 x = - 15$

Combine the opposite terms in $3 x - 10 - 3 x$ .

Subtract $3 x$ from $3 x$ .

$0 - 10 = - 15$

Subtract $10$ from $0$ .

$- 10 = - 15$

Step 5

Since $- 10 \neq - 15$ , there are no solutions.

No solution