Solve for x -1/2(3x-5)=7

$- \frac{1}{2} (3 x - 5) = 7$

Step 1

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{1}{2} \cdot (3 x - 5)) = - 2 \cdot 7$

Step 2

Simplify both sides of the equation.

Simplify the left side.

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

Apply the distributive property.

$- 2 (- \frac{1}{2} (3 x) - \frac{1}{2} \cdot - 5) = - 2 \cdot 7$

Multiply $- \frac{1}{2} (3 x)$ .

Multiply $3$ by $- 1$ .

$- 2 (- 3 (\frac{1}{2}) x - \frac{1}{2} \cdot - 5) = - 2 \cdot 7$

Combine $- 3$ and $\frac{1}{2}$ .

$- 2 (\frac{- 3}{2} x - \frac{1}{2} \cdot - 5) = - 2 \cdot 7$

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

$- 2 (\frac{- 3 x}{2} - \frac{1}{2} \cdot - 5) = - 2 \cdot 7$

Multiply $- \frac{1}{2} \cdot - 5$ .

Multiply $- 5$ by $- 1$ .

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

Combine $5$ and $\frac{1}{2}$ .

$- 2 (\frac{- 3 x}{2} + \frac{5}{2}) = - 2 \cdot 7$

Move the negative in front of the fraction.

$- 2 (- \frac{3 x}{2} + \frac{5}{2}) = - 2 \cdot 7$

Simplify terms.

Apply the distributive property.

$- 2 (- \frac{3 x}{2}) - 2 (\frac{5}{2}) = - 2 \cdot 7$

Cancel the common factor of $2$ .

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

$- 2 \frac{- 3 x}{2} - 2 (\frac{5}{2}) = - 2 \cdot 7$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- 3 x}{2} - 2 (\frac{5}{2}) = - 2 \cdot 7$

Cancel the common factor.

$2 \cdot - 1 \frac{- 3 x}{2} - 2 (\frac{5}{2}) = - 2 \cdot 7$

Rewrite the expression.

$- (- 3 x) - 2 (\frac{5}{2}) = - 2 \cdot 7$

Multiply $- 3$ by $- 1$ .

$3 x - 2 (\frac{5}{2}) = - 2 \cdot 7$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 1$ by $5$ .

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

Simplify the right side.

Multiply $- 2$ by $7$ .

$3 x - 5 = - 14$

Step 3

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

Add $5$ to both sides of the equation.

$3 x = - 14 + 5$

Add $- 14$ and $5$ .

$3 x = - 9$

Step 4

Divide each term in $3 x = - 9$ by $3$ and simplify.

Divide each term in $3 x = - 9$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 9$ by $3$ .

$x = - 3$

Solve for x -1/2(3x-5)=7

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