Pregunta
(4) Solve the equation \( 3(x+6)+2(x+3)=64 \) and find \( x \). \( \begin{array}{llll}\text { (A) } 8 & \text { (B) } 6 & \text { (C) } 4 & \text { (D) } 3\end{array} \)
Ask by Wade Fitzgerald. in the United Arab Emirates
Nov 15,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The correct answer is (A) 8.
Solución
Solve the equation \( 3(x+6)+2(x+3)=64 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(3\left(x+6\right)+2\left(x+3\right)=64\)
- step1: Move the expression to the left side:
\(3\left(x+6\right)+2\left(x+3\right)-64=0\)
- step2: Calculate:
\(5x-40=0\)
- step3: Move the constant to the right side:
\(5x=0+40\)
- step4: Remove 0:
\(5x=40\)
- step5: Divide both sides:
\(\frac{5x}{5}=\frac{40}{5}\)
- step6: Divide the numbers:
\(x=8\)
The solution to the equation \(3(x+6)+2(x+3)=64\) is \(x=8\).
Therefore, the correct answer is (A) 8.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Beyond the Answer
To solve the equation \( 3(x+6)+2(x+3)=64 \), we first distribute the constants: 1. \( 3(x+6) = 3x + 18 \) 2. \( 2(x+3) = 2x + 6 \) Now, we can combine these: \[ 3x + 18 + 2x + 6 = 64 \] Combining like terms gives us: \[ 5x + 24 = 64 \] Next, we isolate \( 5x \) by subtracting 24 from both sides: \[ 5x = 64 - 24 \\ 5x = 40 \] Now, we divide by 5 to solve for \( x \): \[ x = \frac{40}{5} = 8 \] Thus, the solution is \( x = 8 \), which corresponds to option (A).
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