Question

5/12(z-3)=1/3(2z-7)+2

Answer 1

Ответ с решением во вложении

Answer 2

To solve the equation $\frac{5}{12}(z-3) = \frac{1}{3}(2z-7) + 2$ for $z$, follow these steps:

Step 1: Distribute the fractions to simplify the equation:

$\frac{5}{12} \cdot z - \frac{5}{12} \cdot 3 = \frac{1}{3} \cdot 2z - \frac{1}{3} \cdot 7 + 2$

Step 2: Perform the multiplications:

$\frac{5z}{12} - \frac{5}{4} = \frac{2z}{3} - \frac{7}{3} + 2$

Step 3: Get rid of the fractions by multiplying the entire equation by the least common multiple (LCM) of the denominators, which is 12:

$12 \left( \frac{5z}{12} - \frac{5}{4} \right) = 12 \left( \frac{2z}{3} - \frac{7}{3} + 2 \right)$

Step 4: Simplify and solve the resulting equation:

$5z - 15 = 8z - 28 + 24$

Step 5: Move the $8z$ term to the left side and the constants to the right side:

$5z - 8z = -28 + 24 + 15$

Step 6: Combine like terms:

$-3z = 11$

Step 7: Solve for $z$ by dividing both sides by -3:

$z = -\frac{11}{3}$

So, the solution to the equation is $z = -\frac{11}{3}$.