Solve for z -2/3z-1/4=-1/5

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

Step 1

Simplify each term.

Combine $z$ and $\frac{2}{3}$ .

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

Move $2$ to the left of $z$ .

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

Step 2

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

Add $\frac{1}{4}$ to both sides of the equation.

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

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

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

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

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

Multiply $5$ by $4$ .

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

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

$- \frac{2 z}{3} = - \frac{4}{20} + \frac{5}{4 \cdot 5}$

Multiply $4$ by $5$ .

$- \frac{2 z}{3} = - \frac{4}{20} + \frac{5}{20}$

Combine the numerators over the common denominator.

$- \frac{2 z}{3} = \frac{- 4 + 5}{20}$

Add $- 4$ and $5$ .

$- \frac{2 z}{3} = \frac{1}{20}$

Step 3

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

$- \frac{3}{2} (- \frac{2 z}{3}) = - \frac{3}{2} \cdot \frac{1}{20}$

Step 4

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $3$ .

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

$\frac{- 3}{2} (- \frac{2 z}{3}) = - \frac{3}{2} \cdot \frac{1}{20}$

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

$\frac{- 3}{2} \cdot \frac{- 2 z}{3} = - \frac{3}{2} \cdot \frac{1}{20}$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{2} \cdot \frac{- 2 z}{3} = - \frac{3}{2} \cdot \frac{1}{20}$

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{- 2 z}{3} = - \frac{3}{2} \cdot \frac{1}{20}$

Rewrite the expression.

$\frac{- 1}{2} (- 2 z) = - \frac{3}{2} \cdot \frac{1}{20}$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 z$ .

$\frac{- 1}{2} (2 (- z)) = - \frac{3}{2} \cdot \frac{1}{20}$

Cancel the common factor.

$\frac{- 1}{2} (2 (- z)) = - \frac{3}{2} \cdot \frac{1}{20}$

Rewrite the expression.

$- - z = - \frac{3}{2} \cdot \frac{1}{20}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 z = - \frac{3}{2} \cdot \frac{1}{20}$

Multiply $z$ by $1$ .

$z = - \frac{3}{2} \cdot \frac{1}{20}$

Simplify the right side.

Multiply $- \frac{3}{2} \cdot \frac{1}{20}$ .

Multiply $\frac{1}{20}$ by $\frac{3}{2}$ .

$z = - \frac{3}{20 \cdot 2}$

Multiply $20$ by $2$ .

$z = - \frac{3}{40}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{3}{40}$

Decimal Form:

$z = - 0.075$

Solve for z -2/3z-1/4=-1/5

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