Solve for x -5x-3(-7x+3/2)=-(x+6)-3/2

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

Step 1

Simplify $- 5 x - 3 (- 7 x + \frac{3}{2})$ .

Simplify each term.

Apply the distributive property.

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

Multiply $- 7$ by $- 3$ .

$- 5 x + 21 x - 3 (\frac{3}{2}) = - (x + 6) - \frac{3}{2}$

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

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

$- 5 x + 21 x + \frac{- 3 \cdot 3}{2} = - (x + 6) - \frac{3}{2}$

Multiply $- 3$ by $3$ .

$- 5 x + 21 x + \frac{- 9}{2} = - (x + 6) - \frac{3}{2}$

Move the negative in front of the fraction.

$- 5 x + 21 x - \frac{9}{2} = - (x + 6) - \frac{3}{2}$

Add $- 5 x$ and $21 x$ .

$16 x - \frac{9}{2} = - (x + 6) - \frac{3}{2}$

Step 2

Simplify $- (x + 6) - \frac{3}{2}$ .

Simplify each term.

Apply the distributive property.

$16 x - \frac{9}{2} = - x - 1 \cdot 6 - \frac{3}{2}$

Multiply $- 1$ by $6$ .

$16 x - \frac{9}{2} = - x - 6 - \frac{3}{2}$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$16 x - \frac{9}{2} = - x - 6 \cdot \frac{2}{2} - \frac{3}{2}$

Combine $- 6$ and $\frac{2}{2}$ .

$16 x - \frac{9}{2} = - x + \frac{- 6 \cdot 2}{2} - \frac{3}{2}$

Combine the numerators over the common denominator.

$16 x - \frac{9}{2} = - x + \frac{- 6 \cdot 2 - 3}{2}$

Simplify the numerator.

Multiply $- 6$ by $2$ .

$16 x - \frac{9}{2} = - x + \frac{- 12 - 3}{2}$

Subtract $3$ from $- 12$ .

$16 x - \frac{9}{2} = - x + \frac{- 15}{2}$

Move the negative in front of the fraction.

$16 x - \frac{9}{2} = - x - \frac{15}{2}$

Step 3

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

Add $x$ to both sides of the equation.

$16 x - \frac{9}{2} + x = - \frac{15}{2}$

Add $16 x$ and $x$ .

$17 x - \frac{9}{2} = - \frac{15}{2}$

Step 4

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

Add $\frac{9}{2}$ to both sides of the equation.

$17 x = - \frac{15}{2} + \frac{9}{2}$

Combine the numerators over the common denominator.

$17 x = \frac{- 15 + 9}{2}$

Add $- 15$ and $9$ .

$17 x = \frac{- 6}{2}$

Divide $- 6$ by $2$ .

$17 x = - 3$

Step 5

Divide each term in $17 x = - 3$ by $17$ and simplify.

Divide each term in $17 x = - 3$ by $17$ .

$\frac{17 x}{17} = \frac{- 3}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 x}{17} = \frac{- 3}{17}$

Divide $x$ by $1$ .

$x = \frac{- 3}{17}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{17}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{17}$

Decimal Form:

$x = - 0.17647058 \dots$

Solve for x -5x-3(-7x+3/2)=-(x+6)-3/2

Related Questions

Support LCMGCF.com by disabling your adblocker.