Pregunta
What is the value of \( z \) in the equatio \( -\frac{5}{4}(z+8)=-6 ? \) \( z= \)
Ask by Kelly John. in the United States
Nov 01,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( z=-\frac{16}{5} \) or \( z=-3.2 \).
Solución
Solve the equation \( -\frac{5}{4}(z+8)=-6 \).
Solve the equation by following steps:
- step0: Solve for \(z\):
\(-\frac{5}{4}\left(z+8\right)=-6\)
- step1: Multiply the terms:
\(-\frac{5}{4}z-10=-6\)
- step2: Move the constant to the right side:
\(-\frac{5}{4}z=-6+10\)
- step3: Add the numbers:
\(-\frac{5}{4}z=4\)
- step4: Change the signs:
\(\frac{5}{4}z=-4\)
- step5: Multiply by the reciprocal:
\(\frac{5}{4}z\times \frac{4}{5}=-4\times \frac{4}{5}\)
- step6: Multiply:
\(z=-\frac{16}{5}\)
The value of \( z \) in the equation \(-\frac{5}{4}(z+8)=-6\) is \( z=-\frac{16}{5} \) or \( z=-3.2 \).
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Simplifique esta solución The Deep Dive
To find the value of \( z \), let's solve the equation step by step. Starting with the equation: \[ -\frac{5}{4}(z + 8) = -6 \] First, eliminate the negative sign by multiplying both sides by -1: \[ \frac{5}{4}(z + 8) = 6 \] Next, multiply both sides by \( \frac{4}{5} \) to solve for \( z + 8 \): \[ z + 8 = 6 \times \frac{4}{5} = \frac{24}{5} \] Now, subtract 8 from both sides. Since 8 is equivalent to \( \frac{40}{5} \), we have: \[ z = \frac{24}{5} - \frac{40}{5} = \frac{24 - 40}{5} = \frac{-16}{5} \] Therefore, the value of \( z \) is: \[ z = -\frac{16}{5} \]
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