Solve for x 5(-2x+7)+3=-10x+38

$5 (- 2 x + 7) + 3 = - 10 x + 38$

Simplify $5 (- 2 x + 7) + 3$ .

Simplify each term.

Apply the distributive property.

$5 (- 2 x) + 5 \cdot 7 + 3 = - 10 x + 38$

Multiply $- 2$ by $5$ .

$- 10 x + 5 \cdot 7 + 3 = - 10 x + 38$

Multiply $5$ by $7$ .

$- 10 x + 35 + 3 = - 10 x + 38$

Add $35$ and $3$ .

$- 10 x + 38 = - 10 x + 38$

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

Add $10 x$ to both sides of the equation.

$- 10 x + 38 + 10 x = 38$

Combine the opposite terms in $- 10 x + 38 + 10 x$ .

Add $- 10 x$ and $10 x$ .

$0 + 38 = 38$

Add $0$ and $38$ .

$38 = 38$

Since $38 = 38$ , 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:

$(- \infty, \infty)$