Question

13/15z-(7/9+1/3z)=7/2/9​

Answer 1

Ответ:

13/15z-(7/9+1/3z)=7 2/9 13/15z-7/9-1/3z=7 2/9 13/15z-1/3z=7 2/9+7/9 13/15z-5/15z=11 5/18 +14/18 8/15z=12 1/18 z=12 1/18:8/15 z=22 29/48

Answer 2

To solve the equation $\frac{13}{15}z - \left(\frac{7}{9} + \frac{1}{3}z\right) = \frac{7}{2} \div 9$, follow these steps:

Step 1: Simplify the right side of the equation: $\frac{7}{2} \div 9$ can be simplified as follows: $\frac{7}{2} \div 9 = \frac{7}{2} \cdot \frac{1}{9} = \frac{7}{18}$.

So, the equation becomes: $\frac{13}{15}z - \left(\frac{7}{9} + \frac{1}{3}z\right) = \frac{7}{18}$.

Step 2: Distribute the negative sign on the left side of the equation: $\frac{13}{15}z - \frac{7}{9} - \frac{1}{3}z = \frac{7}{18}$.

Step 3: Combine like terms on the left side of the equation. To do this, we need to find a common denominator for $\frac{13}{15}z$ and $-\frac{1}{3}z$, which is 15. So, we can rewrite these fractions with a common denominator: $\frac{13}{15}z - \frac{7}{9} - \frac{5}{15}z = \frac{7}{18}$.

Step 4: Now, we can combine the fractions on the left side: $\left(\frac{13}{15}z - \frac{5}{15}z\right) - \frac{7}{9} = \frac{7}{18}$.

Step 5: Combine the z terms: $\frac{8}{15}z - \frac{7}{9} = \frac{7}{18}$.

Step 6: To eliminate the fractions, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is $15 \cdot 9 \cdot 18 = 2430$: $2430 \cdot \left(\frac{8}{15}z - \frac{7}{9}\right) = 2430 \cdot \frac{7}{18}$.

Step 7: Simplify both sides: $162z - 170z = 425$.

Step 8: Combine like terms on the left side: $-8z = 425$.

Step 9: Divide both sides by -8 to solve for z: $z = \frac{425}{-8}.$

Finally, you can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 1: $z = -\frac{425}{8}.$

So, the solution to the equation is $z = -\frac{425}{8}$.