Solve for x -x+1/2x=67/12+x+5/3-2

$- x + \frac{1}{2} x = \frac{67}{12} + x + \frac{5}{3} - 2$

Step 1

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

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

$- x + \frac{x}{2} = \frac{67}{12} + x + \frac{5}{3} - 2$

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

$- x \cdot \frac{2}{2} + \frac{x}{2} = \frac{67}{12} + x + \frac{5}{3} - 2$

Simplify terms.

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

$\frac{- x \cdot 2}{2} + \frac{x}{2} = \frac{67}{12} + x + \frac{5}{3} - 2$

Combine the numerators over the common denominator.

$\frac{- x \cdot 2 + x}{2} = \frac{67}{12} + x + \frac{5}{3} - 2$

Simplify the numerator.

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

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

$\frac{x (- 1 \cdot 2) + x}{2} = \frac{67}{12} + x + \frac{5}{3} - 2$

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

$\frac{x (- 1 \cdot 2) + x^{1}}{2} = \frac{67}{12} + x + \frac{5}{3} - 2$

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

$\frac{x (- 1 \cdot 2) + x \cdot 1}{2} = \frac{67}{12} + x + \frac{5}{3} - 2$

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

$\frac{x (- 1 \cdot 2 + 1)}{2} = \frac{67}{12} + x + \frac{5}{3} - 2$

Multiply $- 1$ by $2$ .

$\frac{x (- 2 + 1)}{2} = \frac{67}{12} + x + \frac{5}{3} - 2$

Add $- 2$ and $1$ .

$\frac{x \cdot - 1}{2} = \frac{67}{12} + x + \frac{5}{3} - 2$

Simplify the expression.

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

$\frac{- 1 \cdot x}{2} = \frac{67}{12} + x + \frac{5}{3} - 2$

Move the negative in front of the fraction.

$- \frac{x}{2} = \frac{67}{12} + x + \frac{5}{3} - 2$

Step 2

Simplify $\frac{67}{12} + x + \frac{5}{3} - 2$ .

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

$- \frac{x}{2} = x + \frac{67}{12} + \frac{5}{3} \cdot \frac{4}{4} - 2$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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

$- \frac{x}{2} = x + \frac{67}{12} + \frac{5 \cdot 4}{3 \cdot 4} - 2$

Multiply $3$ by $4$ .

$- \frac{x}{2} = x + \frac{67}{12} + \frac{5 \cdot 4}{12} - 2$

Combine the numerators over the common denominator.

$- \frac{x}{2} = x + \frac{67 + 5 \cdot 4}{12} - 2$

Simplify the numerator.

Multiply $5$ by $4$ .

$- \frac{x}{2} = x + \frac{67 + 20}{12} - 2$

Add $67$ and $20$ .

$- \frac{x}{2} = x + \frac{87}{12} - 2$

Cancel the common factor of $87$ and $12$ .

Factor $3$ out of $87$ .

$- \frac{x}{2} = x + \frac{3 (29)}{12} - 2$

Cancel the common factors.

Factor $3$ out of $12$ .

$- \frac{x}{2} = x + \frac{3 \cdot 29}{3 \cdot 4} - 2$

Cancel the common factor.

$- \frac{x}{2} = x + \frac{3 \cdot 29}{3 \cdot 4} - 2$

Rewrite the expression.

$- \frac{x}{2} = x + \frac{29}{4} - 2$

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

$- \frac{x}{2} = x + \frac{29}{4} - 2 \cdot \frac{4}{4}$

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

$- \frac{x}{2} = x + \frac{29}{4} + \frac{- 2 \cdot 4}{4}$

Combine the numerators over the common denominator.

$- \frac{x}{2} = x + \frac{29 - 2 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 2$ by $4$ .

$- \frac{x}{2} = x + \frac{29 - 8}{4}$

Subtract $8$ from $29$ .

$- \frac{x}{2} = x + \frac{21}{4}$

Step 3

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

Subtract $x$ from both sides of the equation.

$- \frac{x}{2} - x = \frac{21}{4}$

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

$- \frac{x}{2} - x \cdot \frac{2}{2} = \frac{21}{4}$

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

$- \frac{x}{2} + \frac{- x \cdot 2}{2} = \frac{21}{4}$

Combine the numerators over the common denominator.

$\frac{- x - x \cdot 2}{2} = \frac{21}{4}$

Simplify the numerator.

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

Factor $x$ out of $- x$ .

$\frac{x \cdot - 1 - x \cdot 2}{2} = \frac{21}{4}$

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

$\frac{x \cdot - 1 + x (- 1 \cdot 2)}{2} = \frac{21}{4}$

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

$\frac{x (- 1 - 1 \cdot 2)}{2} = \frac{21}{4}$

Multiply $- 1$ by $2$ .

$\frac{x (- 1 - 2)}{2} = \frac{21}{4}$

Subtract $2$ from $- 1$ .

$\frac{x \cdot - 3}{2} = \frac{21}{4}$

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

$\frac{- 3 \cdot x}{2} = \frac{21}{4}$

Move the negative in front of the fraction.

$- \frac{3 x}{2} = \frac{21}{4}$

Step 4

Multiply both sides of the equation by $- \frac{2}{3}$ .

$- \frac{2}{3} (- \frac{3 x}{2}) = - \frac{2}{3} \cdot \frac{21}{4}$

Step 5

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- \frac{3 x}{2}) = - \frac{2}{3} \cdot \frac{21}{4}$

Move the leading negative in $- \frac{3 x}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot \frac{21}{4}$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot \frac{21}{4}$

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot \frac{21}{4}$

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{2}{3} \cdot \frac{21}{4}$

Cancel the common factor of $3$ .

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

$\frac{- 1}{3} (3 (- x)) = - \frac{2}{3} \cdot \frac{21}{4}$

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{2}{3} \cdot \frac{21}{4}$

Rewrite the expression.

$- - x = - \frac{2}{3} \cdot \frac{21}{4}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{3} \cdot \frac{21}{4}$

Multiply $x$ by $1$ .

$x = - \frac{2}{3} \cdot \frac{21}{4}$

Simplify the right side.

Simplify $- \frac{2}{3} \cdot \frac{21}{4}$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$x = \frac{- 2}{3} \cdot \frac{21}{4}$

Factor $2$ out of $- 2$ .

$x = \frac{2 (- 1)}{3} \cdot \frac{21}{4}$

Factor $2$ out of $4$ .

$x = \frac{2 \cdot - 1}{3} \cdot \frac{21}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot - 1}{3} \cdot \frac{21}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{- 1}{3} \cdot \frac{21}{2}$

Cancel the common factor of $3$ .

Factor $3$ out of $21$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 3.5$

Mixed Number Form:

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

Solve for x -x+1/2x=67/12+x+5/3-2

Related Questions

Support LCMGCF.com by disabling your adblocker.