Solve for x -4(x-5)+1=-1+3(x+6)

$- 4 (x - 5) + 1 = - 1 + 3 (x + 6)$

Simplify $- 4 (x - 5) + 1$ .

Simplify each term.

Apply the distributive property.

$- 4 x - 4 \cdot - 5 + 1 = - 1 + 3 (x + 6)$

Multiply $- 4$ by $- 5$ .

$- 4 x + 20 + 1 = - 1 + 3 (x + 6)$

Add $20$ and $1$ .

$- 4 x + 21 = - 1 + 3 (x + 6)$

Simplify $- 1 + 3 (x + 6)$ .

Simplify each term.

Apply the distributive property.

$- 4 x + 21 = - 1 + 3 x + 3 \cdot 6$

Multiply $3$ by $6$ .

$- 4 x + 21 = - 1 + 3 x + 18$

Add $- 1$ and $18$ .

$- 4 x + 21 = 3 x + 17$

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

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

$- 4 x + 21 - 3 x = 17$

Subtract $3 x$ from $- 4 x$ .

$- 7 x + 21 = 17$

Move all terms not containing $x$ to the right side of the equation.

Subtract $21$ from both sides of the equation.

$- 7 x = 17 - 21$

Subtract $21$ from $17$ .

$- 7 x = - 4$

Divide each term in $- 7 x = - 4$ by $- 7$ and simplify.

Divide each term in $- 7 x = - 4$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 4}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 4}{- 7}$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 7}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{4}{7}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{7}$

Decimal Form:

$x = 0.\overline{571428}$