Solve for x ((3-4x)-12)/2=2x+3/2

$\frac{(3 - 4 x) - 12}{2} = 2 x + \frac{3}{2}$

Step 1

Multiply both sides by $2$ .

$\frac{3 - 4 x - 12}{2} \cdot 2 = (2 x + \frac{3}{2}) \cdot 2$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{3 - 4 x - 12}{2} \cdot 2$ .

Subtract $12$ from $3$ .

$\frac{- 4 x - 9}{2} \cdot 2 = (2 x + \frac{3}{2}) \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{- 4 x - 9}{2} \cdot 2 = (2 x + \frac{3}{2}) \cdot 2$

Rewrite the expression.

$- 4 x - 9 = (2 x + \frac{3}{2}) \cdot 2$

Simplify the right side.

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

Apply the distributive property.

$- 4 x - 9 = 2 x \cdot 2 + \frac{3}{2} \cdot 2$

Multiply $2$ by $2$ .

$- 4 x - 9 = 4 x + \frac{3}{2} \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 4 x - 9 = 4 x + \frac{3}{2} \cdot 2$

Rewrite the expression.

$- 4 x - 9 = 4 x + 3$

Step 3

Solve for $x$ .

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

Subtract $4 x$ from both sides of the equation.

$- 4 x - 9 - 4 x = 3$

Subtract $4 x$ from $- 4 x$ .

$- 8 x - 9 = 3$

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

Add $9$ to both sides of the equation.

$- 8 x = 3 + 9$

Add $3$ and $9$ .

$- 8 x = 12$

Divide each term in $- 8 x = 12$ by $- 8$ and simplify.

Divide each term in $- 8 x = 12$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{12}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{12}{- 8}$

Divide $x$ by $1$ .

$x = \frac{12}{- 8}$

Simplify the right side.

Cancel the common factor of $12$ and $- 8$ .

Factor $4$ out of $12$ .

$x = \frac{4 (3)}{- 8}$

Cancel the common factors.

Factor $4$ out of $- 8$ .

$x = \frac{4 \cdot 3}{4 \cdot - 2}$

Cancel the common factor.

$x = \frac{4 \cdot 3}{4 \cdot - 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 1.5$

Mixed Number Form:

$x = - 1 \frac{1}{2}$

Solve for x ((3-4x)-12)/2=2x+3/2

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