Pregunta
Solve for \( s \). \( 0.8+s=9(0.2 s+0.8) \) \( s=\square \) Submit
Ask by Lynch Sandoval. in the United States
Feb 03,2025
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\( s = -8 \)
Solución
To solve for \( s \) in the equation:
\[
0.8 + s = 9(0.2s + 0.8)
\]
**Step 1:** Expand the right-hand side.
\[
0.8 + s = 9 \times 0.2s + 9 \times 0.8
\]
\[
0.8 + s = 1.8s + 7.2
\]
**Step 2:** Move all terms involving \( s \) to one side and constant terms to the other side.
\[
0.8 = 1.8s + 7.2 - s
\]
\[
0.8 = 0.8s + 7.2
\]
**Step 3:** Subtract 7.2 from both sides to isolate the terms with \( s \).
\[
0.8 - 7.2 = 0.8s
\]
\[
-6.4 = 0.8s
\]
**Step 4:** Divide both sides by 0.8 to solve for \( s \).
\[
s = \frac{-6.4}{0.8}
\]
\[
s = -8
\]
**Solution:**
\[
s = -8
\]
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The Deep Dive
To solve for \( s \) in the equation \( 0.8+s=9(0.2 s+0.8) \), let's start by expanding the right side: 1. Distribute the 9: \[ 0.8 + s = 1.8s + 7.2 \] 2. Rearranging gives: \[ s - 1.8s = 7.2 - 0.8 \] \[ -0.8s = 6.4 \] 3. To solve for \( s \), divide both sides by -0.8: \[ s = \frac{6.4}{-0.8} \] \[ s = -8 \] Thus, the solution is \( s = -8 \).
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