Solve for x 15x-20=6x-(x+2)+(-x+3)

$15 x - 20 = 6 x - (x + 2) + (- x + 3)$

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

$6 x - (x + 2) - x + 3 = 15 x - 20$

Simplify $6 x - (x + 2) - x + 3$ .

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Simplify each term.

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Apply the distributive property.

$6 x - x - 1 \cdot 2 - x + 3 = 15 x - 20$

Multiply $- 1$ by $2$ .

$6 x - x - 2 - x + 3 = 15 x - 20$

Simplify by adding terms.

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Subtract $x$ from $6 x$ .

$5 x - 2 - x + 3 = 15 x - 20$

Subtract $x$ from $5 x$ .

$4 x - 2 + 3 = 15 x - 20$

Add $- 2$ and $3$ .

$4 x + 1 = 15 x - 20$

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

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Subtract $15 x$ from both sides of the equation.

$4 x + 1 - 15 x = - 20$

Subtract $15 x$ from $4 x$ .

$- 11 x + 1 = - 20$

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

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Subtract $1$ from both sides of the equation.

$- 11 x = - 20 - 1$

Subtract $1$ from $- 20$ .

$- 11 x = - 21$

Divide each term in $- 11 x = - 21$ by $- 11$ and simplify.

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Divide each term in $- 11 x = - 21$ by $- 11$ .

$\frac{- 11 x}{- 11} = \frac{- 21}{- 11}$

Simplify the left side.

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Cancel the common factor of $- 11$ .

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Cancel the common factor.

$\frac{- 11 x}{- 11} = \frac{- 21}{- 11}$

Divide $x$ by $1$ .

$x = \frac{- 21}{- 11}$

Simplify the right side.

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Dividing two negative values results in a positive value.

$x = \frac{21}{11}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{21}{11}$

Decimal Form:

$x = 1.\overline{90}$

Mixed Number Form:

$x = 1 \frac{10}{11}$