Pregunta
Solve the equation. \[ \begin{array}{l}4(2+2 x)=7(x-1) \\ \text { Select the correct choice below and fill in any answer boxes in your choice. } \\ \text { A. The solution set is }\{\square \text {. (Simplify your answer.) } \\ \text { B. There is no solution. }\end{array} \text { } \]
Ask by Bird Henry. in the United States
Jan 31,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The solution set is \(\{-15\}\).
Solución
To solve the equation:
\[
4(2 + 2x) = 7(x - 1)
\]
**Step 1: Expand both sides.**
\[
4 \cdot 2 + 4 \cdot 2x = 7x - 7
\]
\[
8 + 8x = 7x - 7
\]
**Step 2: Move all terms involving \(x\) to one side and constants to the other side.**
\[
8x - 7x = -7 - 8
\]
\[
x = -15
\]
**Conclusion:**
The solution set is \(\{ -15 \}\).
**Answer:**
**A. The solution set is \(\{-15\}\).**
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Simplifique esta solución Extra Insights
To solve the equation \( 4(2+2x)=7(x-1) \), we first expand both sides: 1. Left side: \[ 4(2 + 2x) = 8 + 8x \] 2. Right side: \[ 7(x - 1) = 7x - 7 \] Now, we set the two sides equal to each other: \[ 8 + 8x = 7x - 7 \] Next, we isolate \(x\) by getting all terms involving \(x\) on one side and constant terms on the other: \[ 8x - 7x = -7 - 8 \] Simplifying both sides gives: \[ x = -15 \] Thus, the solution set is \(\{-15\}\). So, the correct choice is: A. The solution set is \(\{-15\}\).
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