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Answer
La solución de la ecuación es \(x=-5\).
Solution
Solve the equation \( 5x+9=3(x-5)+14 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(5x+9=3\left(x-5\right)+14\)
- step1: Move the expression to the left side:
\(5x+9-\left(3\left(x-5\right)+14\right)=0\)
- step2: Calculate:
\(5x-5-3\left(x-5\right)=0\)
- step3: Calculate:
\(2x+10=0\)
- step4: Move the constant to the right side:
\(2x=0-10\)
- step5: Remove 0:
\(2x=-10\)
- step6: Divide both sides:
\(\frac{2x}{2}=\frac{-10}{2}\)
- step7: Divide the numbers:
\(x=-5\)
La solución de la ecuación \(5x+9=3(x-5)+14\) es \(x=-5\).
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Simplify this solution Extra Insights
To solve the equation \( 5x + 9 = 3(x - 5) + 14 \), let's start by distributing on the right side: \[ 5x + 9 = 3x - 15 + 14 \] Simplifying the right side gives us: \[ 5x + 9 = 3x - 1 \] Now, let's isolate \( x \) by moving the \( 3x \) over to the left side and the 9 to the right: \[ 5x - 3x = -1 - 9 \] This simplifies to: \[ 2x = -10 \] Next, we divide both sides by 2: \[ x = -5 \] So, the solution to the equation is \( x = -5 \). Always double-check your answer by plugging \( x \) back into the original equation to ensure both sides are equal!
