Solve for X -1/2X-(-3)-X=15

$- \frac{1}{2} X - (- 3) - X = 15$

Step 1

Simplify $- \frac{1}{2} X - (- 3) - X$ .

Simplify each term.

Combine $X$ and $\frac{1}{2}$ .

$- \frac{X}{2} - (- 3) - X = 15$

Multiply $- 1$ by $- 3$ .

$- \frac{X}{2} + 3 - X = 15$

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

$- \frac{X}{2} - X \cdot \frac{2}{2} + 3 = 15$

Simplify terms.

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

$- \frac{X}{2} + \frac{- X \cdot 2}{2} + 3 = 15$

Combine the numerators over the common denominator.

$\frac{- X - X \cdot 2}{2} + 3 = 15$

Simplify each term.

Simplify the numerator.

Factor $X$ out of $- X - X \cdot 2$ .

Factor $X$ out of $- X$ .

$\frac{X \cdot - 1 - X \cdot 2}{2} + 3 = 15$

Factor $X$ out of $- X \cdot 2$ .

$\frac{X \cdot - 1 + X (- 1 \cdot 2)}{2} + 3 = 15$

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

$\frac{X (- 1 - 1 \cdot 2)}{2} + 3 = 15$

Multiply $- 1$ by $2$ .

$\frac{X (- 1 - 2)}{2} + 3 = 15$

Subtract $2$ from $- 1$ .

$\frac{X \cdot - 3}{2} + 3 = 15$

Move $- 3$ to the left of $X$ .

$\frac{- 3 \cdot X}{2} + 3 = 15$

Move the negative in front of the fraction.

$- \frac{3 X}{2} + 3 = 15$

Step 2

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

Subtract $3$ from both sides of the equation.

$- \frac{3 X}{2} = 15 - 3$

Subtract $3$ from $15$ .

$- \frac{3 X}{2} = 12$

Step 3

Multiply both sides of the equation by $- \frac{2}{3}$ .

$- \frac{2}{3} (- \frac{3 X}{2}) = - \frac{2}{3} \cdot 12$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{3} (- \frac{3 X}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- \frac{3 X}{2}) = - \frac{2}{3} \cdot 12$

Move the leading negative in $- \frac{3 X}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 X}{2} = - \frac{2}{3} \cdot 12$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 X}{2} = - \frac{2}{3} \cdot 12$

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 X}{2} = - \frac{2}{3} \cdot 12$

Rewrite the expression.

$\frac{- 1}{3} (- 3 X) = - \frac{2}{3} \cdot 12$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 X$ .

$\frac{- 1}{3} (3 (- X)) = - \frac{2}{3} \cdot 12$

Cancel the common factor.

$\frac{- 1}{3} (3 (- X)) = - \frac{2}{3} \cdot 12$

Rewrite the expression.

$- - X = - \frac{2}{3} \cdot 12$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 X = - \frac{2}{3} \cdot 12$

Multiply $X$ by $1$ .

$X = - \frac{2}{3} \cdot 12$

Simplify the right side.

Simplify $- \frac{2}{3} \cdot 12$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$X = \frac{- 2}{3} \cdot 12$

Factor $3$ out of $12$ .

$X = \frac{- 2}{3} \cdot (3 (4))$

Cancel the common factor.

$X = \frac{- 2}{3} \cdot (3 \cdot 4)$

Rewrite the expression.

$X = - 2 \cdot 4$

Multiply $- 2$ by $4$ .

$X = - 8$

Solve for X -1/2X-(-3)-X=15

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