Solve for x 5x+3/2=6-2/3x

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

Step 1

Simplify each term.

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

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

Move $2$ to the left of $x$ .

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

Step 2

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

Add $\frac{2 x}{3}$ to both sides of the equation.

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

To write $5 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $5 x \cdot 3 + 2 x$ .

Factor $x$ out of $5 x \cdot 3$ .

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

Factor $x$ out of $2 x$ .

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

Factor $x$ out of $x (5 \cdot 3) + x \cdot 2$ .

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

Multiply $5$ by $3$ .

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

Add $15$ and $2$ .

$\frac{x \cdot 17}{3} + \frac{3}{2} = 6$

Move $17$ to the left of $x$ .

$\frac{17 x}{3} + \frac{3}{2} = 6$

Step 3

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

Subtract $\frac{3}{2}$ from both sides of the equation.

$\frac{17 x}{3} = 6 - \frac{3}{2}$

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

$\frac{17 x}{3} = 6 \cdot \frac{2}{2} - \frac{3}{2}$

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

$\frac{17 x}{3} = \frac{6 \cdot 2}{2} - \frac{3}{2}$

Combine the numerators over the common denominator.

$\frac{17 x}{3} = \frac{6 \cdot 2 - 3}{2}$

Simplify the numerator.

Multiply $6$ by $2$ .

$\frac{17 x}{3} = \frac{12 - 3}{2}$

Subtract $3$ from $12$ .

$\frac{17 x}{3} = \frac{9}{2}$

Step 4

Multiply both sides of the equation by $\frac{3}{17}$ .

$\frac{3}{17} \cdot \frac{17 x}{3} = \frac{3}{17} \cdot \frac{9}{2}$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{17} \cdot \frac{17 x}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{17} \cdot \frac{17 x}{3} = \frac{3}{17} \cdot \frac{9}{2}$

Rewrite the expression.

$\frac{1}{17} (17 x) = \frac{3}{17} \cdot \frac{9}{2}$

Cancel the common factor of $17$ .

Factor $17$ out of $17 x$ .

$\frac{1}{17} (17 (x)) = \frac{3}{17} \cdot \frac{9}{2}$

Cancel the common factor.

$\frac{1}{17} (17 x) = \frac{3}{17} \cdot \frac{9}{2}$

Rewrite the expression.

$x = \frac{3}{17} \cdot \frac{9}{2}$

Simplify the right side.

Multiply $\frac{3}{17} \cdot \frac{9}{2}$ .

Multiply $\frac{3}{17}$ by $\frac{9}{2}$ .

$x = \frac{3 \cdot 9}{17 \cdot 2}$

Multiply $3$ by $9$ .

$x = \frac{27}{17 \cdot 2}$

Multiply $17$ by $2$ .

$x = \frac{27}{34}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{27}{34}$

Decimal Form:

$x = 0.79411764 \dots$

Solve for x 5x+3/2=6-2/3x

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