Solve for x -9/4=2(1/2x+2)-3x

$- \frac{9}{4} = 2 (\frac{1}{2} x + 2) - 3 x$

Step 1

Rewrite the equation as $2 (\frac{1}{2} x + 2) - 3 x = - \frac{9}{4}$ .

$2 (\frac{1}{2} x + 2) - 3 x = - \frac{9}{4}$

Step 2

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

Simplify each term.

Combine $\frac{1}{2}$ and $x$ .

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $2$ .

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

Subtract $3 x$ from $x$ .

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

Step 3

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

Subtract $4$ from both sides of the equation.

$- 2 x = - \frac{9}{4} - 4$

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Combine $- 4$ and $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 4$ by $4$ .

$- 2 x = \frac{- 9 - 16}{4}$

Subtract $16$ from $- 9$ .

$- 2 x = \frac{- 25}{4}$

Move the negative in front of the fraction.

$- 2 x = - \frac{25}{4}$

Step 4

Divide each term in $- 2 x = - \frac{25}{4}$ by $- 2$ and simplify.

Divide each term in $- 2 x = - \frac{25}{4}$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- \frac{25}{4}}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- \frac{25}{4}}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- \frac{25}{4}}{- 2}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{25}{4} \cdot \frac{1}{- 2}$

Move the negative in front of the fraction.

$x = - \frac{25}{4} (- \frac{1}{2})$

Multiply $- \frac{25}{4} (- \frac{1}{2})$ .

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{25}{4}) \frac{1}{2}$

Multiply $\frac{25}{4}$ by $1$ .

$x = \frac{25}{4} \cdot \frac{1}{2}$

Multiply $\frac{25}{4}$ by $\frac{1}{2}$ .

$x = \frac{25}{4 \cdot 2}$

Multiply $4$ by $2$ .

$x = \frac{25}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{25}{8}$

Decimal Form:

$x = 3.125$

Mixed Number Form:

$x = 3 \frac{1}{8}$

Solve for x -9/4=2(1/2x+2)-3x

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