Question
equation. Express your answer as an integer, simplified fraction, or decimal rounded to two decimal plac \[ \frac{13}{12} z-\frac{3}{8}=\frac{11}{8} \]
Ask by Bond Young. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( z = \frac{21}{13} \)
Solution
Subtract \(\frac{3}{8}\) from both sides:
\[
\frac{13}{12} z = \frac{11}{8}+\frac{3}{8} = \frac{11+3}{8} = \frac{14}{8} = \frac{7}{4}.
\]
Multiply both sides by the reciprocal of \(\frac{13}{12}\) (which is \(\frac{12}{13}\)):
\[
z = \frac{7}{4}\cdot \frac{12}{13} = \frac{7\cdot 12}{4\cdot 13}.
\]
Simplify the fraction:
\[
\frac{7\cdot 12}{4\cdot 13} = \frac{7\cdot 3}{13} = \frac{21}{13}.
\]
Thus, the solution is \(\frac{21}{13}\).
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Simplify this solution The Deep Dive
To solve for \( z \), we first need to isolate it. Start by adding \( \frac{3}{8} \) to both sides of the equation: \[ \frac{13}{12} z = \frac{11}{8} + \frac{3}{8} \] Now, add \( \frac{11}{8} \) and \( \frac{3}{8} \) together: \[ \frac{11 + 3}{8} = \frac{14}{8} = \frac{7}{4} \] Now our equation looks like this: \[ \frac{13}{12} z = \frac{7}{4} \] Next, multiply both sides by the reciprocal of \( \frac{13}{12} \) to solve for \( z \): \[ z = \frac{7}{4} \times \frac{12}{13} \] Now let's simplify: \[ z = \frac{7 \times 12}{4 \times 13} = \frac{84}{52} = \frac{21}{13} \] So, the solution is: \[ z = \frac{21}{13} \approx 1.62 \text{ (rounded to two decimal places)} \]
