Solve for x 5/4x+1/2=2x-1/2

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

Step 1

Combine $\frac{5}{4}$ and $x$ .

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

Step 2

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

Subtract $2 x$ from both sides of the equation.

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

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

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

Combine $- 2 x$ and $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $5 x - 2 x \cdot 4$ .

Factor $x$ out of $5 x$ .

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

Factor $x$ out of $- 2 x \cdot 4$ .

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

Factor $x$ out of $x \cdot 5 + x (- 2 \cdot 4)$ .

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

Multiply $- 2$ by $4$ .

$\frac{x (5 - 8)}{4} + \frac{1}{2} = - \frac{1}{2}$

Subtract $8$ from $5$ .

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

Move $- 3$ to the left of $x$ .

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

Move the negative in front of the fraction.

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

Step 3

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

Subtract $\frac{1}{2}$ from both sides of the equation.

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $- 1$ .

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

Divide $- 2$ by $2$ .

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

Step 4

Multiply both sides of the equation by $- \frac{4}{3}$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

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

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

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

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Multiply $- \frac{4}{3} \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

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

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

$x = \frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{3}$

Decimal Form:

$x = 1.\overline{3}$

Mixed Number Form:

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

Solve for x 5/4x+1/2=2x-1/2

Related Questions

Support LCMGCF.com by disabling your adblocker.