Question
Solve for \( z \). \[ 2+\frac{7}{z}=\frac{2}{5} \] Simplify your answer as much as possible. \[ z= \] No solution ㅁ,
Ask by Morrison Weston. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( z = -\frac{35}{8} \)
Solution
We start with the equation:
2 + (7/z) = 2/5.
Step 1: Subtract 2 from both sides to isolate the fraction.
7/z = (2/5) − 2.
Step 2: Express 2 with a denominator of 5:
2 = 10/5,
so 7/z = (2/5) − (10/5) = -8/5.
Step 3: Cross multiply to solve for z (assuming z ≠ 0):
7 = (-8/5)z
⇒ z = 7 / (-8/5)
⇒ z = 7 × (-5/8)
⇒ z = -35/8.
Thus, the solution is:
z = -35/8.
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Simplify this solution Extra Insights
To solve for \( z \), start by subtracting 2 from both sides of the equation: \[ \frac{7}{z} = \frac{2}{5} - 2 \] Convert 2 into a fraction with a denominator of 5: \[ 2 = \frac{10}{5} \] Now substitute this back into the equation: \[ \frac{7}{z} = \frac{2}{5} - \frac{10}{5} = \frac{-8}{5} \] Next, cross-multiply to solve for \( z \): \[ 7 \cdot 5 = -8z \] Which simplifies to: \[ 35 = -8z \] Isolate \( z \) by dividing both sides by -8: \[ z = -\frac{35}{8} \] So, the final answer is: \[ z = -\frac{35}{8} \]
