Solve for x x-2(2-3/2x)=2(4-x)+10

$x - 2 (2 - \frac{3}{2} x) = 2 (4 - x) + 10$

Step 1

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

Simplify each term.

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

$x - 2 (2 - \frac{x \cdot 3}{2}) = 2 (4 - x) + 10$

Move $3$ to the left of $x$ .

$x - 2 (2 - \frac{3 x}{2}) = 2 (4 - x) + 10$

Apply the distributive property.

$x - 2 \cdot 2 - 2 (- \frac{3 x}{2}) = 2 (4 - x) + 10$

Multiply $- 2$ by $2$ .

$x - 4 - 2 (- \frac{3 x}{2}) = 2 (4 - x) + 10$

Cancel the common factor of $2$ .

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

$x - 4 - 2 \frac{- 3 x}{2} = 2 (4 - x) + 10$

Factor $2$ out of $- 2$ .

$x - 4 + 2 (- 1) \frac{- 3 x}{2} = 2 (4 - x) + 10$

Cancel the common factor.

$x - 4 + 2 \cdot - 1 \frac{- 3 x}{2} = 2 (4 - x) + 10$

Rewrite the expression.

$x - 4 - 1 (- 3 x) = 2 (4 - x) + 10$

Multiply $- 3$ by $- 1$ .

$x - 4 + 3 x = 2 (4 - x) + 10$

Add $x$ and $3 x$ .

$4 x - 4 = 2 (4 - x) + 10$

Step 2

Simplify $2 (4 - x) + 10$ .

Simplify each term.

Apply the distributive property.

$4 x - 4 = 2 \cdot 4 + 2 (- x) + 10$

Multiply $2$ by $4$ .

$4 x - 4 = 8 + 2 (- x) + 10$

Multiply $- 1$ by $2$ .

$4 x - 4 = 8 - 2 x + 10$

Add $8$ and $10$ .

$4 x - 4 = - 2 x + 18$

Step 3

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

Add $2 x$ to both sides of the equation.

$4 x - 4 + 2 x = 18$

Add $4 x$ and $2 x$ .

$6 x - 4 = 18$

Step 4

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

Add $4$ to both sides of the equation.

$6 x = 18 + 4$

Add $18$ and $4$ .

$6 x = 22$

Step 5

Divide each term in $6 x = 22$ by $6$ and simplify.

Divide each term in $6 x = 22$ by $6$ .

$\frac{6 x}{6} = \frac{22}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{22}{6}$

Divide $x$ by $1$ .

$x = \frac{22}{6}$

Simplify the right side.

Cancel the common factor of $22$ and $6$ .

Factor $2$ out of $22$ .

$x = \frac{2 (11)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$x = \frac{2 \cdot 11}{2 \cdot 3}$

Cancel the common factor.

$x = \frac{2 \cdot 11}{2 \cdot 3}$

Rewrite the expression.

$x = \frac{11}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{3}$

Decimal Form:

$x = 3.\overline{6}$

Mixed Number Form:

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

Solve for x x-2(2-3/2x)=2(4-x)+10

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