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

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

Simplify $\frac{7 (x - 1)}{2} - 5 x$ .

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $7$ by $- 1$ .

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

Multiply $2$ by $- 5$ .

$\frac{7 x - 7 - 10 x}{2} = \frac{1}{2}$

Subtract $10 x$ from $7 x$ .

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

Simplify with factoring out.

Factor $- 1$ out of $- 3 x$ .

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

Rewrite $- 7$ as $- 1 (7)$ .

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

Factor $- 1$ out of $- (3 x) - 1 (7)$ .

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

Simplify the expression.

Rewrite $- (3 x + 7)$ as $- 1 (3 x + 7)$ .

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

Move the negative in front of the fraction.

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

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

$- (3 x + 7) = 1$

Simplify $- (3 x + 7)$ .

Apply the distributive property.

$- (3 x) - 1 \cdot 7 = 1$

Multiply.

Multiply $3$ by $- 1$ .

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

Multiply $- 1$ by $7$ .

$- 3 x - 7 = 1$

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

Add $7$ to both sides of the equation.

$- 3 x = 1 + 7$

Add $1$ and $7$ .

$- 3 x = 8$

Divide each term in $- 3 x = 8$ by $- 3$ and simplify.

Divide each term in $- 3 x = 8$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{8}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{8}{- 3}$

Divide $x$ by $1$ .

$x = \frac{8}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{8}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{8}{3}$

Decimal Form:

$x = - 2.\overline{6}$

Mixed Number Form:

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

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

Related Questions

Support LCMGCF.com by disabling your adblocker.