Pregunta
The movement of the progress bar may be uneven because Solve for \( x: 4|2 x-5|+6=10 \)
Ask by Washington Delgado. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The solutions are \( x=2 \) and \( x=3 \).
Solución
Solve the equation \( 4|2x-5|+6=10 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(4\left|2x-5\right|+6=10\)
- step1: Move the expression to the left side:
\(4\left|2x-5\right|+6-10=0\)
- step2: Subtract the numbers:
\(4\left|2x-5\right|-4=0\)
- step3: Separate into possible cases:
\(\begin{align}&4\left(2x-5\right)-4=0,2x-5\geq 0\\&4\left(-\left(2x-5\right)\right)-4=0,2x-5<0\end{align}\)
- step4: Solve the equation:
\(\begin{align}&x=3,x\geq \frac{5}{2}\\&x=2,x<\frac{5}{2}\end{align}\)
- step5: Find the intersection:
\(\begin{align}&x=3\\&x=2\end{align}\)
- step6: Rewrite:
\(x_{1}=2,x_{2}=3\)
The solutions to the equation \(4|2x-5|+6=10\) are \(x=2\) and \(x=3\).
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Mind Expander
To solve the equation \( 4|2x-5|+6=10 \), start by isolating the absolute value expression. Subtract 6 from both sides: \[ 4|2x-5| = 4 \] Now, divide both sides by 4: \[ |2x-5| = 1 \] This means that the expression inside the absolute value can equal either 1 or -1. So we have two cases to consider: 1. \( 2x - 5 = 1 \) 2. \( 2x - 5 = -1 \) For the first case: \[ 2x - 5 = 1 \] Adding 5 to both sides: \[ 2x = 6 \] Dividing by 2 gives: \[ x = 3 \] For the second case: \[ 2x - 5 = -1 \] Adding 5 to both sides: \[ 2x = 4 \] Dividing by 2 gives: \[ x = 2 \] So the solutions are \( x = 3 \) and \( x = 2 \).
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