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

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

Step 1

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

Rewrite.

$x + \frac{3}{2} = 0 + 0 + \frac{3}{4} \cdot (x - \frac{1}{2})$

Simplify by adding zeros.

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

Apply the distributive property.

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

Combine $\frac{3}{4}$ and $x$ .

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

Multiply $\frac{3}{4} (- \frac{1}{2})$ .

Multiply $\frac{3}{4}$ by $\frac{1}{2}$ .

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

Multiply $4$ by $2$ .

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

Step 2

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

Subtract $\frac{3 x}{4}$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Subtract $3 x$ from $x \cdot 4$ .

Reorder $x$ and $4$ .

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

Subtract $3 x$ from $4 \cdot x$ .

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

Step 3

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

Subtract $\frac{3}{2}$ from both sides of the equation.

$\frac{x}{4} = - \frac{3}{8} - \frac{3}{2}$

To write $- \frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{4} = - \frac{3}{8} - \frac{3}{2} \cdot \frac{4}{4}$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{2}$ by $\frac{4}{4}$ .

$\frac{x}{4} = - \frac{3}{8} - \frac{3 \cdot 4}{2 \cdot 4}$

Multiply $2$ by $4$ .

$\frac{x}{4} = - \frac{3}{8} - \frac{3 \cdot 4}{8}$

Combine the numerators over the common denominator.

$\frac{x}{4} = \frac{- 3 - 3 \cdot 4}{8}$

Simplify the numerator.

Multiply $- 3$ by $4$ .

$\frac{x}{4} = \frac{- 3 - 12}{8}$

Subtract $12$ from $- 3$ .

$\frac{x}{4} = \frac{- 15}{8}$

Move the negative in front of the fraction.

$\frac{x}{4} = - \frac{15}{8}$

Step 4

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 (- \frac{15}{8})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{x}{4} = 4 (- \frac{15}{8})$

Rewrite the expression.

$x = 4 (- \frac{15}{8})$

Simplify the right side.

Simplify $4 (- \frac{15}{8})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{15}{8}$ into the numerator.

$x = 4 (\frac{- 15}{8})$

Factor $4$ out of $8$ .

$x = 4 \frac{- 15}{4 (2)}$

Cancel the common factor.

$x = 4 \frac{- 15}{4 \cdot 2}$

Rewrite the expression.

$x = \frac{- 15}{2}$

Move the negative in front of the fraction.

$x = - \frac{15}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{15}{2}$

Decimal Form:

$x = - 7.5$

Mixed Number Form:

$x = - 7 \frac{1}{2}$

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

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