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

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

Step 1

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

Simplify each term.

Apply the distributive property.

$2 x - (5 x) - 1 \cdot 3 = 7 + 3 x - 2$

Multiply $5$ by $- 1$ .

$2 x - 5 x - 1 \cdot 3 = 7 + 3 x - 2$

Multiply $- 1$ by $3$ .

$2 x - 5 x - 3 = 7 + 3 x - 2$

Subtract $5 x$ from $2 x$ .

$- 3 x - 3 = 7 + 3 x - 2$

Step 2

Subtract $2$ from $7$ .

$- 3 x - 3 = 3 x + 5$

Step 3

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

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

$- 3 x - 3 - 3 x = 5$

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

$- 6 x - 3 = 5$

Step 4

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

Add $3$ to both sides of the equation.

$- 6 x = 5 + 3$

Add $5$ and $3$ .

$- 6 x = 8$

Step 5

Divide each term in $- 6 x = 8$ by $- 6$ and simplify.

Divide each term in $- 6 x = 8$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{8}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{8}{- 6}$

Divide $x$ by $1$ .

$x = \frac{8}{- 6}$

Simplify the right side.

Cancel the common factor of $8$ and $- 6$ .

Factor $2$ out of $8$ .

$x = \frac{2 (4)}{- 6}$

Cancel the common factors.

Factor $2$ out of $- 6$ .

$x = \frac{2 \cdot 4}{2 \cdot - 3}$

Cancel the common factor.

$x = \frac{2 \cdot 4}{2 \cdot - 3}$

Rewrite the expression.

$x = \frac{4}{- 3}$

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{3}$

Decimal Form:

$x = - 1.\overline{3}$

Mixed Number Form:

$x = - 1 \frac{1}{3}$

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

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