Solve for x 2x-(3-2x)/3=2

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

Step 1

Simplify $2 x - \frac{3 - 2 x}{3}$ .

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

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

Apply the distributive property.

$\frac{6 x - 1 \cdot 3 - (- 2 x)}{3} = 2$

Multiply $- 1$ by $3$ .

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

Multiply $- 2$ by $- 1$ .

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

Add $6 x$ and $2 x$ .

$\frac{8 x - 3}{3} = 2$

Step 2

Multiply both sides by $3$ .

$\frac{8 x - 3}{3} \cdot 3 = 2 \cdot 3$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{8 x - 3}{3} \cdot 3 = 2 \cdot 3$

Rewrite the expression.

$8 x - 3 = 2 \cdot 3$

Simplify the right side.

Multiply $2$ by $3$ .

$8 x - 3 = 6$

Step 4

Solve for $x$ .

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

Add $3$ to both sides of the equation.

$8 x = 6 + 3$

Add $6$ and $3$ .

$8 x = 9$

Divide each term in $8 x = 9$ by $8$ and simplify.

Divide each term in $8 x = 9$ by $8$ .

$\frac{8 x}{8} = \frac{9}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{9}{8}$

Divide $x$ by $1$ .

$x = \frac{9}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{8}$

Decimal Form:

$x = 1.125$

Mixed Number Form:

$x = 1 \frac{1}{8}$

Solve for x 2x-(3-2x)/3=2

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