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

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

Step 1

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

Simplify each term.

Apply the distributive property.

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

Multiply $- 3$ by $- 1$ .

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

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

Raise $x$ to the power of $1$ .

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

Factor $x$ out of $x^{1}$ .

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

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

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

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

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

Multiply $- 3$ by $2$ .

$\frac{x (1 - 6)}{2} + 3 = 5 x - 7$

Subtract $6$ from $1$ .

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

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

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

Move the negative in front of the fraction.

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

Step 2

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

Subtract $5 x$ from both sides of the equation.

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

To write $- 5 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

Factor $5 x$ out of $- 5 x$ .

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

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

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

Factor $5 x$ out of $5 x (- 1) + 5 x (- 1 \cdot 2)$ .

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

Multiply $- 1$ by $2$ .

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

Subtract $2$ from $- 1$ .

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

Multiply $- 3$ by $5$ .

$\frac{- 15 x}{2} + 3 = - 7$

Move the negative in front of the fraction.

$- \frac{15 x}{2} + 3 = - 7$

Step 3

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

Subtract $3$ from both sides of the equation.

$- \frac{15 x}{2} = - 7 - 3$

Subtract $3$ from $- 7$ .

$- \frac{15 x}{2} = - 10$

Step 4

Multiply both sides of the equation by $- \frac{2}{15}$ .

$- \frac{2}{15} (- \frac{15 x}{2}) = - \frac{2}{15} \cdot - 10$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{15} (- \frac{15 x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{15}$ into the numerator.

$\frac{- 2}{15} (- \frac{15 x}{2}) = - \frac{2}{15} \cdot - 10$

Move the leading negative in $- \frac{15 x}{2}$ into the numerator.

$\frac{- 2}{15} \cdot \frac{- 15 x}{2} = - \frac{2}{15} \cdot - 10$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{15} \cdot \frac{- 15 x}{2} = - \frac{2}{15} \cdot - 10$

Cancel the common factor.

$\frac{2 \cdot - 1}{15} \cdot \frac{- 15 x}{2} = - \frac{2}{15} \cdot - 10$

Rewrite the expression.

$\frac{- 1}{15} (- 15 x) = - \frac{2}{15} \cdot - 10$

Cancel the common factor of $15$ .

Factor $15$ out of $- 15 x$ .

$\frac{- 1}{15} (15 (- x)) = - \frac{2}{15} \cdot - 10$

Cancel the common factor.

$\frac{- 1}{15} (15 (- x)) = - \frac{2}{15} \cdot - 10$

Rewrite the expression.

$- - x = - \frac{2}{15} \cdot - 10$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{15} \cdot - 10$

Multiply $x$ by $1$ .

$x = - \frac{2}{15} \cdot - 10$

Simplify the right side.

Simplify $- \frac{2}{15} \cdot - 10$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{2}{15}$ into the numerator.

$x = \frac{- 2}{15} \cdot - 10$

Factor $5$ out of $15$ .

$x = \frac{- 2}{5 (3)} \cdot - 10$

Factor $5$ out of $- 10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Multiply $- 2$ by $- 2$ .

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

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

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