Solve for x -3/2(1/3x+3)-x=-10-5x

$- \frac{3}{2} (\frac{1}{3} x + 3) - x = - 10 - 5 x$

Step 1

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

Simplify each term.

Combine $\frac{1}{3}$ and $x$ .

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

Apply the distributive property.

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

Cancel the common factor of $3$ .

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

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

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{2} \cdot \frac{x}{3} - \frac{3}{2} \cdot 3 - x = - 10 - 5 x$

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{x}{3} - \frac{3}{2} \cdot 3 - x = - 10 - 5 x$

Rewrite the expression.

$\frac{- 1}{2} x - \frac{3}{2} \cdot 3 - x = - 10 - 5 x$

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

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

Multiply $- \frac{3}{2} \cdot 3$ .

Multiply $3$ by $- 1$ .

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

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

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

Multiply $- 3$ by $3$ .

$\frac{- x}{2} + \frac{- 9}{2} - x = - 10 - 5 x$

Simplify each term.

Move the negative in front of the fraction.

$- \frac{x}{2} + \frac{- 9}{2} - x = - 10 - 5 x$

Move the negative in front of the fraction.

$- \frac{x}{2} - \frac{9}{2} - x = - 10 - 5 x$

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

$- \frac{x}{2} - x \cdot \frac{2}{2} - \frac{9}{2} = - 10 - 5 x$

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

$- \frac{x}{2} + \frac{- x \cdot 2}{2} - \frac{9}{2} = - 10 - 5 x$

Combine the numerators over the common denominator.

$\frac{- x - x \cdot 2}{2} - \frac{9}{2} = - 10 - 5 x$

Combine the numerators over the common denominator.

$\frac{- x - x \cdot 2 - 9}{2} = - 10 - 5 x$

Multiply $2$ by $- 1$ .

$\frac{- x - 2 x - 9}{2} = - 10 - 5 x$

Subtract $2 x$ from $- x$ .

$\frac{- 3 x - 9}{2} = - 10 - 5 x$

Factor $3$ out of $- 3 x - 9$ .

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

$\frac{3 (- x) - 9}{2} = - 10 - 5 x$

Factor $3$ out of $- 9$ .

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

Factor $3$ out of $3 (- x) + 3 (- 3)$ .

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

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

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

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{3 (- (x) - 1 (3))}{2} = - 10 - 5 x$

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

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

Simplify the expression.

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

$\frac{3 (- 1 (x + 3))}{2} = - 10 - 5 x$

Move the negative in front of the fraction.

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

Step 2

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

Add $5 x$ to both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $- 3$ by $3$ .

$\frac{- 3 x - 9 + 5 x \cdot 2}{2} = - 10$

Multiply $2$ by $5$ .

$\frac{- 3 x - 9 + 10 x}{2} = - 10$

Add $- 3 x$ and $10 x$ .

$\frac{7 x - 9}{2} = - 10$

Step 3

Multiply both sides by $2$ .

$\frac{7 x - 9}{2} \cdot 2 = - 10 \cdot 2$

Step 4

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7 x - 9}{2} \cdot 2 = - 10 \cdot 2$

Rewrite the expression.

$7 x - 9 = - 10 \cdot 2$

Simplify the right side.

Multiply $- 10$ by $2$ .

$7 x - 9 = - 20$

Step 5

Solve for $x$ .

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

Add $9$ to both sides of the equation.

$7 x = - 20 + 9$

Add $- 20$ and $9$ .

$7 x = - 11$

Divide each term in $7 x = - 11$ by $7$ and simplify.

Divide each term in $7 x = - 11$ by $7$ .

$\frac{7 x}{7} = \frac{- 11}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 11}{7}$

Divide $x$ by $1$ .

$x = \frac{- 11}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{11}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{11}{7}$

Decimal Form:

$x = - 1.\overline{571428}$

Mixed Number Form:

$x = - 1 \frac{4}{7}$

Solve for x -3/2(1/3x+3)-x=-10-5x

Related Questions

Support LCMGCF.com by disabling your adblocker.