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

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

Step 1

Simplify the left side.

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

Convert $1 \frac{2}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

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

Add $1$ and $\frac{2}{3}$ .

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add $3$ and $2$ .

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

Apply the distributive property.

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

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

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

Multiply $- \frac{1}{4} \cdot \frac{5}{3}$ .

Multiply $\frac{5}{3}$ by $\frac{1}{4}$ .

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

Multiply $3$ by $4$ .

$- \frac{x}{4} - \frac{5}{12} = - 2 \frac{1}{5}$

Step 2

Simplify the right side.

Convert $2 \frac{1}{5}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$- \frac{x}{4} - \frac{5}{12} = - (2 + \frac{1}{5})$

Add $2$ and $\frac{1}{5}$ .

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

$- \frac{x}{4} - \frac{5}{12} = - (2 \cdot \frac{5}{5} + \frac{1}{5})$

Combine $2$ and $\frac{5}{5}$ .

$- \frac{x}{4} - \frac{5}{12} = - (\frac{2 \cdot 5}{5} + \frac{1}{5})$

Combine the numerators over the common denominator.

$- \frac{x}{4} - \frac{5}{12} = - \frac{2 \cdot 5 + 1}{5}$

Simplify the numerator.

Multiply $2$ by $5$ .

$- \frac{x}{4} - \frac{5}{12} = - \frac{10 + 1}{5}$

Add $10$ and $1$ .

$- \frac{x}{4} - \frac{5}{12} = - \frac{11}{5}$

Step 3

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

Add $\frac{5}{12}$ to both sides of the equation.

$- \frac{x}{4} = - \frac{11}{5} + \frac{5}{12}$

To write $- \frac{11}{5}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$- \frac{x}{4} = - \frac{11}{5} \cdot \frac{12}{12} + \frac{5}{12}$

To write $\frac{5}{12}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{x}{4} = - \frac{11}{5} \cdot \frac{12}{12} + \frac{5}{12} \cdot \frac{5}{5}$

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{11}{5}$ by $\frac{12}{12}$ .

$- \frac{x}{4} = - \frac{11 \cdot 12}{5 \cdot 12} + \frac{5}{12} \cdot \frac{5}{5}$

Multiply $5$ by $12$ .

$- \frac{x}{4} = - \frac{11 \cdot 12}{60} + \frac{5}{12} \cdot \frac{5}{5}$

Multiply $\frac{5}{12}$ by $\frac{5}{5}$ .

$- \frac{x}{4} = - \frac{11 \cdot 12}{60} + \frac{5 \cdot 5}{12 \cdot 5}$

Multiply $12$ by $5$ .

$- \frac{x}{4} = - \frac{11 \cdot 12}{60} + \frac{5 \cdot 5}{60}$

Combine the numerators over the common denominator.

$- \frac{x}{4} = \frac{- 11 \cdot 12 + 5 \cdot 5}{60}$

Simplify the numerator.

Multiply $- 11$ by $12$ .

$- \frac{x}{4} = \frac{- 132 + 5 \cdot 5}{60}$

Multiply $5$ by $5$ .

$- \frac{x}{4} = \frac{- 132 + 25}{60}$

Add $- 132$ and $25$ .

$- \frac{x}{4} = \frac{- 107}{60}$

Move the negative in front of the fraction.

$- \frac{x}{4} = - \frac{107}{60}$

Step 4

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{x}{4}) = - 4 (- \frac{107}{60})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $4$ .

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

$- 4 \frac{- x}{4} = - 4 (- \frac{107}{60})$

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- x}{4} = - 4 (- \frac{107}{60})$

Cancel the common factor.

$4 \cdot - 1 \frac{- x}{4} = - 4 (- \frac{107}{60})$

Rewrite the expression.

$- - x = - 4 (- \frac{107}{60})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 4 (- \frac{107}{60})$

Multiply $x$ by $1$ .

$x = - 4 (- \frac{107}{60})$

Simplify the right side.

Simplify $- 4 (- \frac{107}{60})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{107}{60}$ into the numerator.

$x = - 4 (\frac{- 107}{60})$

Factor $4$ out of $- 4$ .

$x = 4 (- 1) \frac{- 107}{60}$

Factor $4$ out of $60$ .

$x = 4 \cdot - 1 \frac{- 107}{4 \cdot 15}$

Cancel the common factor.

$x = 4 \cdot - 1 \frac{- 107}{4 \cdot 15}$

Rewrite the expression.

$x = - \frac{- 107}{15}$

Move the negative in front of the fraction.

$x = - - \frac{107}{15}$

Multiply $- - \frac{107}{15}$ .

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{107}{15})$

Multiply $\frac{107}{15}$ by $1$ .

$x = \frac{107}{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{107}{15}$

Decimal Form:

$x = 7.1\overline{3}$

Mixed Number Form:

$x = 7 \frac{2}{15}$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.