Solve for x 3/2(4x-1)+8x=-(4x+1/2)+4x

$\frac{3}{2} (4 x - 1) + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Simplify $\frac{3}{2} \cdot (4 x - 1) + 8 x$ .

Rewrite.

$\frac{3}{2} \cdot (4 x - 1) + 8 x + 4 x = - (4 x + \frac{1}{2}) + 4 x$

Rewrite.

$\frac{3}{2} \cdot (4 x - 1) + 8 x + 4 x - 4 x = - (4 x + \frac{1}{2}) + 4 x$

Simplify by adding terms.

$\frac{3}{2} \cdot (4 x - 1) + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Simplify each term.

Apply the distributive property.

$\frac{3}{2} (4 x) + \frac{3}{2} \cdot - 1 + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Cancel the common factor of $2$ .

Factor $2$ out of $4 x$ .

$\frac{3}{2} (2 (2 x)) + \frac{3}{2} \cdot - 1 + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Cancel the common factor.

$\frac{3}{2} (2 (2 x)) + \frac{3}{2} \cdot - 1 + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Rewrite the expression.

$3 (2 x) + \frac{3}{2} \cdot - 1 + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Multiply $2$ by $3$ .

$6 x + \frac{3}{2} \cdot - 1 + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Multiply $\frac{3}{2} \cdot - 1$ .

Combine $\frac{3}{2}$ and $- 1$ .

$6 x + \frac{3 \cdot - 1}{2} + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Multiply $3$ by $- 1$ .

$6 x + \frac{- 3}{2} + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Move the negative in front of the fraction.

$6 x - \frac{3}{2} + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Add $6 x$ and $8 x$ .

$14 x - \frac{3}{2} = - (4 x + \frac{1}{2}) + 4 x$

Simplify $- (4 x + \frac{1}{2}) + 4 x$ .

Simplify each term.

Apply the distributive property.

$14 x - \frac{3}{2} = - (4 x) - \frac{1}{2} + 4 x$

Multiply $4$ by $- 1$ .

$14 x - \frac{3}{2} = - 4 x - \frac{1}{2} + 4 x$

Combine the opposite terms in $- 4 x - \frac{1}{2} + 4 x$ .

Add $- 4 x$ and $4 x$ .

$14 x - \frac{3}{2} = 0 - \frac{1}{2}$

Subtract $\frac{1}{2}$ from $0$ .

$14 x - \frac{3}{2} = - \frac{1}{2}$

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

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

$14 x = - \frac{1}{2} + \frac{3}{2}$

Combine the numerators over the common denominator.

$14 x = \frac{- 1 + 3}{2}$

Add $- 1$ and $3$ .

$14 x = \frac{2}{2}$

Divide $2$ by $2$ .

$14 x = 1$

Divide each term in $14 x = 1$ by $14$ and simplify.

Divide each term in $14 x = 1$ by $14$ .

$\frac{14 x}{14} = \frac{1}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 x}{14} = \frac{1}{14}$

Divide $x$ by $1$ .

$x = \frac{1}{14}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{14}$

Decimal Form:

$x = 0.0\overline{714285}$

Solve for x 3/2(4x-1)+8x=-(4x+1/2)+4x

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