Solve for x 3/2(10x-6/5)+2x=-x

$\frac{3}{2} (10 x - \frac{6}{5}) + 2 x = - x$

Simplify $\frac{3}{2} \cdot (10 x - \frac{6}{5}) + 2 x$ .

Simplify each term.

Apply the distributive property.

$\frac{3}{2} (10 x) + \frac{3}{2} (- \frac{6}{5}) + 2 x = - x$

Cancel the common factor of $2$ .

Factor $2$ out of $10 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $5$ by $3$ .

$15 x + \frac{3}{2} (- \frac{6}{5}) + 2 x = - x$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$15 x + \frac{3}{2} \cdot \frac{- 6}{5} + 2 x = - x$

Factor $2$ out of $- 6$ .

$15 x + \frac{3}{2} \cdot \frac{2 (- 3)}{5} + 2 x = - x$

Cancel the common factor.

$15 x + \frac{3}{2} \cdot \frac{2 \cdot - 3}{5} + 2 x = - x$

Rewrite the expression.

$15 x + 3 (\frac{- 3}{5}) + 2 x = - x$

Combine $3$ and $\frac{- 3}{5}$ .

$15 x + \frac{3 \cdot - 3}{5} + 2 x = - x$

Multiply $3$ by $- 3$ .

$15 x + \frac{- 9}{5} + 2 x = - x$

Move the negative in front of the fraction.

$15 x - \frac{9}{5} + 2 x = - x$

Add $15 x$ and $2 x$ .

$17 x - \frac{9}{5} = - x$

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

Add $x$ to both sides of the equation.

$17 x - \frac{9}{5} + x = 0$

Add $17 x$ and $x$ .

$18 x - \frac{9}{5} = 0$

Add $\frac{9}{5}$ to both sides of the equation.

$18 x = \frac{9}{5}$

Divide each term in $18 x = \frac{9}{5}$ by $18$ and simplify.

Divide each term in $18 x = \frac{9}{5}$ by $18$ .

$\frac{18 x}{18} = \frac{\frac{9}{5}}{18}$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 x}{18} = \frac{\frac{9}{5}}{18}$

Divide $x$ by $1$ .

$x = \frac{\frac{9}{5}}{18}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{9}{5} \cdot \frac{1}{18}$

Cancel the common factor of $9$ .

Factor $9$ out of $18$ .

$x = \frac{9}{5} \cdot \frac{1}{9 (2)}$

Cancel the common factor.

$x = \frac{9}{5} \cdot \frac{1}{9 \cdot 2}$

Rewrite the expression.

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

Multiply $\frac{1}{5}$ by $\frac{1}{2}$ .

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

Multiply $5$ by $2$ .

$x = \frac{1}{10}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{10}$

Decimal Form:

$x = 0.1$

Solve for x 3/2(10x-6/5)+2x=-x

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