Pregunta
Solve for \( k \) \( 10 k-10=5(3 k+5) \) \( k=\square \)
Ask by Carrillo Vaughn. in the United States
Jan 10,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( k = -7 \)
Solución
To solve for \( k \) in the equation:
\[
10k - 10 = 5(3k + 5)
\]
**Step 1: Expand the right side of the equation**
\[
10k - 10 = 15k + 25
\]
**Step 2: Move all terms involving \( k \) to one side and constants to the other side**
Subtract \( 10k \) from both sides:
\[
-10 = 15k - 10k + 25
\]
\[
-10 = 5k + 25
\]
Subtract \( 25 \) from both sides:
\[
-10 - 25 = 5k
\]
\[
-35 = 5k
\]
**Step 3: Solve for \( k \)**
Divide both sides by \( 5 \):
\[
k = \frac{-35}{5}
\]
\[
k = -7
\]
**Answer:**
\[
k = -7
\]
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Simplifique esta solución Beyond the Answer
To solve for \( k \) in the equation \( 10k - 10 = 5(3k + 5) \), start by distributing the 5 on the right side: \[ 10k - 10 = 15k + 25. \] Next, get all the terms involving \( k \) on one side and constant terms on the other: \[ 10k - 15k = 25 + 10. \] This simplifies to: \[ -5k = 35. \] Now, divide both sides by -5: \[ k = -7. \] So, \( k = -7 \) is the solution!
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