Solve for x 1/4(x-2)=3/5x+1/2

$\frac{1}{4} (x - 2) = \frac{3}{5} x + \frac{1}{2}$

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

Rewrite.

$0 + 0 + \frac{1}{4} \cdot (x - 2) = \frac{3}{5} x + \frac{1}{2}$

Simplify by adding zeros.

$\frac{1}{4} \cdot (x - 2) = \frac{3}{5} x + \frac{1}{2}$

Apply the distributive property.

$\frac{1}{4} x + \frac{1}{4} \cdot - 2 = \frac{3}{5} x + \frac{1}{2}$

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} + \frac{1}{4} \cdot - 2 = \frac{3}{5} x + \frac{1}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{x}{4} + \frac{1}{2 (2)} \cdot - 2 = \frac{3}{5} x + \frac{1}{2}$

Factor $2$ out of $- 2$ .

$\frac{x}{4} + \frac{1}{2 \cdot 2} \cdot (2 \cdot - 1) = \frac{3}{5} x + \frac{1}{2}$

Cancel the common factor.

$\frac{x}{4} + \frac{1}{2 \cdot 2} \cdot (2 \cdot - 1) = \frac{3}{5} x + \frac{1}{2}$

Rewrite the expression.

$\frac{x}{4} + \frac{1}{2} \cdot - 1 = \frac{3}{5} x + \frac{1}{2}$

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

$\frac{x}{4} + \frac{- 1}{2} = \frac{3}{5} x + \frac{1}{2}$

Move the negative in front of the fraction.

$\frac{x}{4} - \frac{1}{2} = \frac{3}{5} x + \frac{1}{2}$

Combine $\frac{3}{5}$ and $x$ .

$\frac{x}{4} - \frac{1}{2} = \frac{3 x}{5} + \frac{1}{2}$

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

Subtract $\frac{3 x}{5}$ from both sides of the equation.

$\frac{x}{4} - \frac{1}{2} - \frac{3 x}{5} = \frac{1}{2}$

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{4} \cdot \frac{5}{5} - \frac{3 x}{5} - \frac{1}{2} = \frac{1}{2}$

To write $- \frac{3 x}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{4} \cdot \frac{5}{5} - \frac{3 x}{5} \cdot \frac{4}{4} - \frac{1}{2} = \frac{1}{2}$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{4}$ by $\frac{5}{5}$ .

$\frac{x \cdot 5}{4 \cdot 5} - \frac{3 x}{5} \cdot \frac{4}{4} - \frac{1}{2} = \frac{1}{2}$

Multiply $4$ by $5$ .

$\frac{x \cdot 5}{20} - \frac{3 x}{5} \cdot \frac{4}{4} - \frac{1}{2} = \frac{1}{2}$

Multiply $\frac{3 x}{5}$ by $\frac{4}{4}$ .

$\frac{x \cdot 5}{20} - \frac{3 x \cdot 4}{5 \cdot 4} - \frac{1}{2} = \frac{1}{2}$

Multiply $5$ by $4$ .

$\frac{x \cdot 5}{20} - \frac{3 x \cdot 4}{20} - \frac{1}{2} = \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{x \cdot 5 - 3 x \cdot 4}{20} - \frac{1}{2} = \frac{1}{2}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x \cdot 5 - 3 x \cdot 4$ .

Factor $x$ out of $x \cdot 5$ .

$\frac{x (5) - 3 x \cdot 4}{20} - \frac{1}{2} = \frac{1}{2}$

Factor $x$ out of $- 3 x \cdot 4$ .

$\frac{x (5) + x (- 3 \cdot 4)}{20} - \frac{1}{2} = \frac{1}{2}$

Factor $x$ out of $x (5) + x (- 3 \cdot 4)$ .

$\frac{x (5 - 3 \cdot 4)}{20} - \frac{1}{2} = \frac{1}{2}$

Multiply $- 3$ by $4$ .

$\frac{x (5 - 12)}{20} - \frac{1}{2} = \frac{1}{2}$

Subtract $12$ from $5$ .

$\frac{x \cdot - 7}{20} - \frac{1}{2} = \frac{1}{2}$

Move $- 7$ to the left of $x$ .

$\frac{- 7 \cdot x}{20} - \frac{1}{2} = \frac{1}{2}$

Move the negative in front of the fraction.

$- \frac{7 x}{20} - \frac{1}{2} = \frac{1}{2}$

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

Add $\frac{1}{2}$ to both sides of the equation.

$- \frac{7 x}{20} = \frac{1}{2} + \frac{1}{2}$

Combine the numerators over the common denominator.

$- \frac{7 x}{20} = \frac{1 + 1}{2}$

Add $1$ and $1$ .

$- \frac{7 x}{20} = \frac{2}{2}$

Divide $2$ by $2$ .

$- \frac{7 x}{20} = 1$

Multiply both sides of the equation by $- \frac{20}{7}$ .

$- \frac{20}{7} (- \frac{7 x}{20}) = - \frac{20}{7} \cdot 1$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{20}{7} (- \frac{7 x}{20})$ .

Cancel the common factor of $20$ .

Move the leading negative in $- \frac{20}{7}$ into the numerator.

$\frac{- 20}{7} (- \frac{7 x}{20}) = - \frac{20}{7} \cdot 1$

Move the leading negative in $- \frac{7 x}{20}$ into the numerator.

$\frac{- 20}{7} \cdot \frac{- 7 x}{20} = - \frac{20}{7} \cdot 1$

Factor $20$ out of $- 20$ .

$\frac{20 (- 1)}{7} \cdot \frac{- 7 x}{20} = - \frac{20}{7} \cdot 1$

Cancel the common factor.

$\frac{20 \cdot - 1}{7} \cdot \frac{- 7 x}{20} = - \frac{20}{7} \cdot 1$

Rewrite the expression.

$\frac{- 1}{7} (- 7 x) = - \frac{20}{7} \cdot 1$

Cancel the common factor of $7$ .

Factor $7$ out of $- 7 x$ .

$\frac{- 1}{7} (7 (- x)) = - \frac{20}{7} \cdot 1$

Cancel the common factor.

$\frac{- 1}{7} (7 (- x)) = - \frac{20}{7} \cdot 1$

Rewrite the expression.

$- - x = - \frac{20}{7} \cdot 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{20}{7} \cdot 1$

Multiply $x$ by $1$ .

$x = - \frac{20}{7} \cdot 1$

Simplify the right side.

Multiply $- 1$ by $1$ .

$x = - \frac{20}{7}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{20}{7}$

Decimal Form:

$x = - 2.\overline{857142}$

Mixed Number Form:

$x = - 2 \frac{6}{7}$

Solve for x 1/4(x-2)=3/5x+1/2

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