Solve for x -3x-(-5/2x+1)=-9-(3x+1/2)

$- 3 x - (- \frac{5}{2} x + 1) = - 9 - (3 x + \frac{1}{2})$

Simplify $- 3 x - (- \frac{5}{2} x + 1)$ .

Simplify each term.

Combine $x$ and $\frac{5}{2}$ .

$- 3 x - (- \frac{x \cdot 5}{2} + 1) = - 9 - (3 x + \frac{1}{2})$

Move $5$ to the left of $x$ .

$- 3 x - (- \frac{5 x}{2} + 1) = - 9 - (3 x + \frac{1}{2})$

Apply the distributive property.

$- 3 x - - \frac{5 x}{2} - 1 \cdot 1 = - 9 - (3 x + \frac{1}{2})$

Multiply $- - \frac{5 x}{2}$ .

Multiply $- 1$ by $- 1$ .

$- 3 x + 1 \frac{5 x}{2} - 1 \cdot 1 = - 9 - (3 x + \frac{1}{2})$

Multiply $\frac{5 x}{2}$ by $1$ .

$- 3 x + \frac{5 x}{2} - 1 \cdot 1 = - 9 - (3 x + \frac{1}{2})$

Multiply $- 1$ by $1$ .

$- 3 x + \frac{5 x}{2} - 1 = - 9 - (3 x + \frac{1}{2})$

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 3 x \cdot \frac{2}{2} + \frac{5 x}{2} - 1 = - 9 - (3 x + \frac{1}{2})$

Simplify terms.

Combine $- 3 x$ and $\frac{2}{2}$ .

$\frac{- 3 x \cdot 2}{2} + \frac{5 x}{2} - 1 = - 9 - (3 x + \frac{1}{2})$

Combine the numerators over the common denominator.

$\frac{- 3 x \cdot 2 + 5 x}{2} - 1 = - 9 - (3 x + \frac{1}{2})$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 3 x \cdot 2 + 5 x$ .

Factor $x$ out of $- 3 x \cdot 2$ .

$\frac{x (- 3 \cdot 2) + 5 x}{2} - 1 = - 9 - (3 x + \frac{1}{2})$

Factor $x$ out of $5 x$ .

$\frac{x (- 3 \cdot 2) + x \cdot 5}{2} - 1 = - 9 - (3 x + \frac{1}{2})$

Factor $x$ out of $x (- 3 \cdot 2) + x \cdot 5$ .

$\frac{x (- 3 \cdot 2 + 5)}{2} - 1 = - 9 - (3 x + \frac{1}{2})$

Multiply $- 3$ by $2$ .

$\frac{x (- 6 + 5)}{2} - 1 = - 9 - (3 x + \frac{1}{2})$

Add $- 6$ and $5$ .

$\frac{x \cdot - 1}{2} - 1 = - 9 - (3 x + \frac{1}{2})$

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{2} - 1 = - 9 - (3 x + \frac{1}{2})$

Move the negative in front of the fraction.

$- \frac{x}{2} - 1 = - 9 - (3 x + \frac{1}{2})$

Simplify $- 9 - (3 x + \frac{1}{2})$ .

Simplify each term.

Apply the distributive property.

$- \frac{x}{2} - 1 = - 9 - (3 x) - \frac{1}{2}$

Multiply $3$ by $- 1$ .

$- \frac{x}{2} - 1 = - 9 - 3 x - \frac{1}{2}$

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x}{2} - 1 = - 3 x - 9 \cdot \frac{2}{2} - \frac{1}{2}$

Combine $- 9$ and $\frac{2}{2}$ .

$- \frac{x}{2} - 1 = - 3 x + \frac{- 9 \cdot 2}{2} - \frac{1}{2}$

Combine the numerators over the common denominator.

$- \frac{x}{2} - 1 = - 3 x + \frac{- 9 \cdot 2 - 1}{2}$

Simplify the numerator.

Multiply $- 9$ by $2$ .

$- \frac{x}{2} - 1 = - 3 x + \frac{- 18 - 1}{2}$

Subtract $1$ from $- 18$ .

$- \frac{x}{2} - 1 = - 3 x + \frac{- 19}{2}$

Move the negative in front of the fraction.

$- \frac{x}{2} - 1 = - 3 x - \frac{19}{2}$

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

Add $3 x$ to both sides of the equation.

$- \frac{x}{2} - 1 + 3 x = - \frac{19}{2}$

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x}{2} + 3 x \cdot \frac{2}{2} - 1 = - \frac{19}{2}$

Combine $3 x$ and $\frac{2}{2}$ .

$- \frac{x}{2} + \frac{3 x \cdot 2}{2} - 1 = - \frac{19}{2}$

Combine the numerators over the common denominator.

$\frac{- x + 3 x \cdot 2}{2} - 1 = - \frac{19}{2}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- x + 3 x \cdot 2$ .

Factor $x$ out of $- x$ .

$\frac{x \cdot - 1 + 3 x \cdot 2}{2} - 1 = - \frac{19}{2}$

Factor $x$ out of $3 x \cdot 2$ .

$\frac{x \cdot - 1 + x (3 \cdot 2)}{2} - 1 = - \frac{19}{2}$

Factor $x$ out of $x \cdot - 1 + x (3 \cdot 2)$ .

$\frac{x (- 1 + 3 \cdot 2)}{2} - 1 = - \frac{19}{2}$

Multiply $3$ by $2$ .

$\frac{x (- 1 + 6)}{2} - 1 = - \frac{19}{2}$

Add $- 1$ and $6$ .

$\frac{x \cdot 5}{2} - 1 = - \frac{19}{2}$

Move $5$ to the left of $x$ .

$\frac{5 x}{2} - 1 = - \frac{19}{2}$

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

Add $1$ to both sides of the equation.

$\frac{5 x}{2} = - \frac{19}{2} + 1$

Write $1$ as a fraction with a common denominator.

$\frac{5 x}{2} = - \frac{19}{2} + \frac{2}{2}$

Combine the numerators over the common denominator.

$\frac{5 x}{2} = \frac{- 19 + 2}{2}$

Add $- 19$ and $2$ .

$\frac{5 x}{2} = \frac{- 17}{2}$

Move the negative in front of the fraction.

$\frac{5 x}{2} = - \frac{17}{2}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$5 x = - 17$

Divide each term in $5 x = - 17$ by $5$ and simplify.

Divide each term in $5 x = - 17$ by $5$ .

$\frac{5 x}{5} = \frac{- 17}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 17}{5}$

Divide $x$ by $1$ .

$x = \frac{- 17}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{17}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{17}{5}$

Decimal Form:

$x = - 3.4$

Mixed Number Form:

$x = - 3 \frac{2}{5}$

Solve for x -3x-(-5/2x+1)=-9-(3x+1/2)

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