Solve for x -1/2-7(x-2)=5(-4x-3)+5/2

$- \frac{1}{2} - 7 (x - 2) = 5 (- 4 x - 3) + \frac{5}{2}$

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

Simplify each term.

Apply the distributive property.

$- \frac{1}{2} - 7 x - 7 \cdot - 2 = 5 (- 4 x - 3) + \frac{5}{2}$

Multiply $- 7$ by $- 2$ .

$- \frac{1}{2} - 7 x + 14 = 5 (- 4 x - 3) + \frac{5}{2}$

To write $14$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 7 x - \frac{1}{2} + 14 \cdot \frac{2}{2} = 5 (- 4 x - 3) + \frac{5}{2}$

Combine $14$ and $\frac{2}{2}$ .

$- 7 x - \frac{1}{2} + \frac{14 \cdot 2}{2} = 5 (- 4 x - 3) + \frac{5}{2}$

Combine the numerators over the common denominator.

$- 7 x + \frac{- 1 + 14 \cdot 2}{2} = 5 (- 4 x - 3) + \frac{5}{2}$

Simplify the numerator.

Multiply $14$ by $2$ .

$- 7 x + \frac{- 1 + 28}{2} = 5 (- 4 x - 3) + \frac{5}{2}$

Add $- 1$ and $28$ .

$- 7 x + \frac{27}{2} = 5 (- 4 x - 3) + \frac{5}{2}$

Simplify $5 (- 4 x - 3) + \frac{5}{2}$ .

Simplify each term.

Apply the distributive property.

$- 7 x + \frac{27}{2} = 5 (- 4 x) + 5 \cdot - 3 + \frac{5}{2}$

Multiply $- 4$ by $5$ .

$- 7 x + \frac{27}{2} = - 20 x + 5 \cdot - 3 + \frac{5}{2}$

Multiply $5$ by $- 3$ .

$- 7 x + \frac{27}{2} = - 20 x - 15 + \frac{5}{2}$

To write $- 15$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 7 x + \frac{27}{2} = - 20 x - 15 \cdot \frac{2}{2} + \frac{5}{2}$

Combine $- 15$ and $\frac{2}{2}$ .

$- 7 x + \frac{27}{2} = - 20 x + \frac{- 15 \cdot 2}{2} + \frac{5}{2}$

Combine the numerators over the common denominator.

$- 7 x + \frac{27}{2} = - 20 x + \frac{- 15 \cdot 2 + 5}{2}$

Simplify the numerator.

Multiply $- 15$ by $2$ .

$- 7 x + \frac{27}{2} = - 20 x + \frac{- 30 + 5}{2}$

Add $- 30$ and $5$ .

$- 7 x + \frac{27}{2} = - 20 x + \frac{- 25}{2}$

Move the negative in front of the fraction.

$- 7 x + \frac{27}{2} = - 20 x - \frac{25}{2}$

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

Add $20 x$ to both sides of the equation.

$- 7 x + \frac{27}{2} + 20 x = - \frac{25}{2}$

Add $- 7 x$ and $20 x$ .

$13 x + \frac{27}{2} = - \frac{25}{2}$

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

Subtract $\frac{27}{2}$ from both sides of the equation.

$13 x = - \frac{25}{2} - \frac{27}{2}$

Combine the numerators over the common denominator.

$13 x = \frac{- 25 - 27}{2}$

Subtract $27$ from $- 25$ .

$13 x = \frac{- 52}{2}$

Divide $- 52$ by $2$ .

$13 x = - 26$

Divide each term in $13 x = - 26$ by $13$ and simplify.

Divide each term in $13 x = - 26$ by $13$ .

$\frac{13 x}{13} = \frac{- 26}{13}$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} = \frac{- 26}{13}$

Divide $x$ by $1$ .

$x = \frac{- 26}{13}$

Simplify the right side.

Divide $- 26$ by $13$ .

$x = - 2$

Solve for x -1/2-7(x-2)=5(-4x-3)+5/2

Related Questions

Support LCMGCF.com by disabling your adblocker.