Solve for x 4(3x-1)+7-x=2x+3+9x

$4 (3 x - 1) + 7 - x = 2 x + 3 + 9 x$

Step 1

Simplify $4 (3 x - 1) + 7 - x$ .

Simplify each term.

Apply the distributive property.

$4 (3 x) + 4 \cdot - 1 + 7 - x = 2 x + 3 + 9 x$

Multiply $3$ by $4$ .

$12 x + 4 \cdot - 1 + 7 - x = 2 x + 3 + 9 x$

Multiply $4$ by $- 1$ .

$12 x - 4 + 7 - x = 2 x + 3 + 9 x$

Simplify by adding terms.

Subtract $x$ from $12 x$ .

$11 x - 4 + 7 = 2 x + 3 + 9 x$

Add $- 4$ and $7$ .

$11 x + 3 = 2 x + 3 + 9 x$

Step 2

Add $2 x$ and $9 x$ .

$11 x + 3 = 11 x + 3$

Step 3

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

Subtract $11 x$ from both sides of the equation.

$11 x + 3 - 11 x = 3$

Combine the opposite terms in $11 x + 3 - 11 x$ .

Subtract $11 x$ from $11 x$ .

$0 + 3 = 3$

Add $0$ and $3$ .

$3 = 3$

Step 4

Since $3 = 3$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$