Solve for z (2z)/3-(3z)/4+(4z)/5-(5z)/6<7

$\frac{2 z}{3} - \frac{3 z}{4} + \frac{4 z}{5} - \frac{5 z}{6} < 7$

Step 1

Simplify $\frac{2 z}{3} - \frac{3 z}{4} + \frac{4 z}{5} - \frac{5 z}{6}$ .

Find the common denominator.

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

$\frac{2 z}{3} \cdot \frac{20}{20} - \frac{3 z}{4} + \frac{4 z}{5} - \frac{5 z}{6} < 7$

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

$\frac{2 z \cdot 20}{3 \cdot 20} - \frac{3 z}{4} + \frac{4 z}{5} - \frac{5 z}{6} < 7$

Multiply $\frac{3 z}{4}$ by $\frac{15}{15}$ .

$\frac{2 z \cdot 20}{3 \cdot 20} - (\frac{3 z}{4} \cdot \frac{15}{15}) + \frac{4 z}{5} - \frac{5 z}{6} < 7$

Multiply $\frac{3 z}{4}$ by $\frac{15}{15}$ .

$\frac{2 z \cdot 20}{3 \cdot 20} - \frac{3 z \cdot 15}{4 \cdot 15} + \frac{4 z}{5} - \frac{5 z}{6} < 7$

Multiply $\frac{4 z}{5}$ by $\frac{12}{12}$ .

$\frac{2 z \cdot 20}{3 \cdot 20} - \frac{3 z \cdot 15}{4 \cdot 15} + \frac{4 z}{5} \cdot \frac{12}{12} - \frac{5 z}{6} < 7$

Multiply $\frac{4 z}{5}$ by $\frac{12}{12}$ .

$\frac{2 z \cdot 20}{3 \cdot 20} - \frac{3 z \cdot 15}{4 \cdot 15} + \frac{4 z \cdot 12}{5 \cdot 12} - \frac{5 z}{6} < 7$

Multiply $\frac{5 z}{6}$ by $\frac{10}{10}$ .

$\frac{2 z \cdot 20}{3 \cdot 20} - \frac{3 z \cdot 15}{4 \cdot 15} + \frac{4 z \cdot 12}{5 \cdot 12} - (\frac{5 z}{6} \cdot \frac{10}{10}) < 7$

Multiply $\frac{5 z}{6}$ by $\frac{10}{10}$ .

$\frac{2 z \cdot 20}{3 \cdot 20} - \frac{3 z \cdot 15}{4 \cdot 15} + \frac{4 z \cdot 12}{5 \cdot 12} - \frac{5 z \cdot 10}{6 \cdot 10} < 7$

Multiply $3$ by $20$ .

$\frac{2 z \cdot 20}{60} - \frac{3 z \cdot 15}{4 \cdot 15} + \frac{4 z \cdot 12}{5 \cdot 12} - \frac{5 z \cdot 10}{6 \cdot 10} < 7$

Multiply $4$ by $15$ .

$\frac{2 z \cdot 20}{60} - \frac{3 z \cdot 15}{60} + \frac{4 z \cdot 12}{5 \cdot 12} - \frac{5 z \cdot 10}{6 \cdot 10} < 7$

Multiply $5$ by $12$ .

$\frac{2 z \cdot 20}{60} - \frac{3 z \cdot 15}{60} + \frac{4 z \cdot 12}{60} - \frac{5 z \cdot 10}{6 \cdot 10} < 7$

Multiply $6$ by $10$ .

$\frac{2 z \cdot 20}{60} - \frac{3 z \cdot 15}{60} + \frac{4 z \cdot 12}{60} - \frac{5 z \cdot 10}{60} < 7$

Combine the numerators over the common denominator.

$\frac{2 z \cdot 20 - 3 z \cdot 15 + 4 z \cdot 12 - 5 z \cdot 10}{60} < 7$

Simplify each term.

Multiply $20$ by $2$ .

$\frac{40 z - 3 z \cdot 15 + 4 z \cdot 12 - 5 z \cdot 10}{60} < 7$

Multiply $15$ by $- 3$ .

$\frac{40 z - 45 z + 4 z \cdot 12 - 5 z \cdot 10}{60} < 7$

Multiply $12$ by $4$ .

$\frac{40 z - 45 z + 48 z - 5 z \cdot 10}{60} < 7$

Multiply $10$ by $- 5$ .

$\frac{40 z - 45 z + 48 z - 50 z}{60} < 7$

Simplify by adding terms.

Subtract $45 z$ from $40 z$ .

$\frac{- 5 z + 48 z - 50 z}{60} < 7$

Add $- 5 z$ and $48 z$ .

$\frac{43 z - 50 z}{60} < 7$

Subtract $50 z$ from $43 z$ .

$\frac{- 7 z}{60} < 7$

Move the negative in front of the fraction.

$- \frac{7 z}{60} < 7$

Step 2

Divide each term in $- \frac{7 z}{60} < 7$ by $- 1$ and simplify.

Divide each term in $- \frac{7 z}{60} < 7$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{7 z}{60}}{- 1} > \frac{7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{7 z}{60}}{1} > \frac{7}{- 1}$

Divide $\frac{7 z}{60}$ by $1$ .

$\frac{7 z}{60} > \frac{7}{- 1}$

Simplify the right side.

Divide $7$ by $- 1$ .

$\frac{7 z}{60} > - 7$

Step 3

Multiply both sides by $60$ .

$\frac{7 z}{60} \cdot 60 > - 7 \cdot 60$

Step 4

Simplify.

Simplify the left side.

Cancel the common factor of $60$ .

Cancel the common factor.

$\frac{7 z}{60} \cdot 60 > - 7 \cdot 60$

Rewrite the expression.

$7 z > - 7 \cdot 60$

Simplify the right side.

Multiply $- 7$ by $60$ .

$7 z > - 420$

Step 5

Divide each term in $7 z > - 420$ by $7$ and simplify.

Divide each term in $7 z > - 420$ by $7$ .

$\frac{7 z}{7} > \frac{- 420}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 z}{7} > \frac{- 420}{7}$

Divide $z$ by $1$ .

$z > \frac{- 420}{7}$

Simplify the right side.

Divide $- 420$ by $7$ .

$z > - 60$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$z > - 60$

Interval Notation:

$(- 60, \infty)$

Solve for z (2z)/3-(3z)/4+(4z)/5-(5z)/6<7

Related Questions

Support LCMGCF.com by disabling your adblocker.