Solve for x (2x)/4-5/3=x-7/2

$\frac{2 x}{4} - \frac{5}{3} = x - \frac{7}{2}$

Step 1

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{4} - \frac{5}{3} = x - \frac{7}{2}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 x}{2 \cdot 2} - \frac{5}{3} = x - \frac{7}{2}$

Cancel the common factor.

$\frac{2 x}{2 \cdot 2} - \frac{5}{3} = x - \frac{7}{2}$

Rewrite the expression.

$\frac{x}{2} - \frac{5}{3} = x - \frac{7}{2}$

Step 2

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

Subtract $x$ from both sides of the equation.

$\frac{x}{2} - \frac{5}{3} - x = - \frac{7}{2}$

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

$\frac{x}{2} - x \cdot \frac{2}{2} - \frac{5}{3} = - \frac{7}{2}$

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

$\frac{x}{2} + \frac{- x \cdot 2}{2} - \frac{5}{3} = - \frac{7}{2}$

Combine the numerators over the common denominator.

$\frac{x - x \cdot 2}{2} - \frac{5}{3} = - \frac{7}{2}$

Simplify each term.

Simplify the numerator.

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

Raise $x$ to the power of $1$ .

$\frac{x^{1} - x \cdot 2}{2} - \frac{5}{3} = - \frac{7}{2}$

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - x \cdot 2}{2} - \frac{5}{3} = - \frac{7}{2}$

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

$\frac{x \cdot 1 + x (- 1 \cdot 2)}{2} - \frac{5}{3} = - \frac{7}{2}$

Factor $x$ out of $x \cdot 1 + x (- 1 \cdot 2)$ .

$\frac{x (1 - 1 \cdot 2)}{2} - \frac{5}{3} = - \frac{7}{2}$

Multiply $- 1$ by $2$ .

$\frac{x (1 - 2)}{2} - \frac{5}{3} = - \frac{7}{2}$

Subtract $2$ from $1$ .

$\frac{x \cdot - 1}{2} - \frac{5}{3} = - \frac{7}{2}$

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{2} - \frac{5}{3} = - \frac{7}{2}$

Move the negative in front of the fraction.

$- \frac{x}{2} - \frac{5}{3} = - \frac{7}{2}$

Step 3

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

Add $\frac{5}{3}$ to both sides of the equation.

$- \frac{x}{2} = - \frac{7}{2} + \frac{5}{3}$

To write $- \frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{x}{2} = - \frac{7}{2} \cdot \frac{3}{3} + \frac{5}{3}$

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x}{2} = - \frac{7}{2} \cdot \frac{3}{3} + \frac{5}{3} \cdot \frac{2}{2}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7}{2}$ by $\frac{3}{3}$ .

$- \frac{x}{2} = - \frac{7 \cdot 3}{2 \cdot 3} + \frac{5}{3} \cdot \frac{2}{2}$

Multiply $2$ by $3$ .

$- \frac{x}{2} = - \frac{7 \cdot 3}{6} + \frac{5}{3} \cdot \frac{2}{2}$

Multiply $\frac{5}{3}$ by $\frac{2}{2}$ .

$- \frac{x}{2} = - \frac{7 \cdot 3}{6} + \frac{5 \cdot 2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$- \frac{x}{2} = - \frac{7 \cdot 3}{6} + \frac{5 \cdot 2}{6}$

Combine the numerators over the common denominator.

$- \frac{x}{2} = \frac{- 7 \cdot 3 + 5 \cdot 2}{6}$

Simplify the numerator.

Multiply $- 7$ by $3$ .

$- \frac{x}{2} = \frac{- 21 + 5 \cdot 2}{6}$

Multiply $5$ by $2$ .

$- \frac{x}{2} = \frac{- 21 + 10}{6}$

Add $- 21$ and $10$ .

$- \frac{x}{2} = \frac{- 11}{6}$

Move the negative in front of the fraction.

$- \frac{x}{2} = - \frac{11}{6}$

Step 4

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{x}{2}) = - 2 (- \frac{11}{6})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$- 2 \frac{- x}{2} = - 2 (- \frac{11}{6})$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- x}{2} = - 2 (- \frac{11}{6})$

Cancel the common factor.

$2 \cdot - 1 \frac{- x}{2} = - 2 (- \frac{11}{6})$

Rewrite the expression.

$- - x = - 2 (- \frac{11}{6})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 2 (- \frac{11}{6})$

Multiply $x$ by $1$ .

$x = - 2 (- \frac{11}{6})$

Simplify the right side.

Simplify $- 2 (- \frac{11}{6})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{11}{6}$ into the numerator.

$x = - 2 (\frac{- 11}{6})$

Factor $2$ out of $- 2$ .

$x = 2 (- 1) \frac{- 11}{6}$

Factor $2$ out of $6$ .

$x = 2 \cdot - 1 \frac{- 11}{2 \cdot 3}$

Cancel the common factor.

$x = 2 \cdot - 1 \frac{- 11}{2 \cdot 3}$

Rewrite the expression.

$x = - \frac{- 11}{3}$

Move the negative in front of the fraction.

$x = - - \frac{11}{3}$

Multiply $- - \frac{11}{3}$ .

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{11}{3})$

Multiply $\frac{11}{3}$ by $1$ .

$x = \frac{11}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{3}$

Decimal Form:

$x = 3.\overline{6}$

Mixed Number Form:

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

Solve for x (2x)/4-5/3=x-7/2

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