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

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

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

Simplify each term.

Apply the distributive property.

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

Multiply $5$ by $- 3$ .

$5 x - 15 + x = 3 (2 x - 5)$

Add $5 x$ and $x$ .

$6 x - 15 = 3 (2 x - 5)$

Simplify $3 (2 x - 5)$ .

Apply the distributive property.

$6 x - 15 = 3 (2 x) + 3 \cdot - 5$

Multiply.

Multiply $2$ by $3$ .

$6 x - 15 = 6 x + 3 \cdot - 5$

Multiply $3$ by $- 5$ .

$6 x - 15 = 6 x - 15$

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

Subtract $6 x$ from both sides of the equation.

$6 x - 15 - 6 x = - 15$

Combine the opposite terms in $6 x - 15 - 6 x$ .

Subtract $6 x$ from $6 x$ .

$0 - 15 = - 15$

Subtract $15$ from $0$ .

$- 15 = - 15$

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:

$(- \infty, \infty)$