Pregunta
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The equation has no solution.
Solución
Solve the equation \( -(-8p+3)=-7p+3(4+5p) \).
Solve the equation by following steps:
- step0: Solve for \(p\):
\(-\left(-8p+3\right)=-7p+3\left(4+5p\right)\)
- step1: Calculate:
\(8p-3=-7p+3\left(4+5p\right)\)
- step2: Move the expression to the left side:
\(8p-3-\left(-7p+3\left(4+5p\right)\right)=0\)
- step3: Subtract the terms:
\(-15=0\)
- step4: The statement is false:
\(p \in \varnothing \)
The equation \( -(-8p+3)=-7p+3(4+5p) \) has no solution.
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Beyond the Answer
Let's expand and simplify the equation step-by-step: First, the left side becomes: \[ -(-8p + 3) = 8p - 3. \] Now for the right side, distribute the \(3\) into \((4 + 5p)\): \[ -7p + 3(4 + 5p) = -7p + 12 + 15p. \] Now combine like terms on the right side: \[ -7p + 15p + 12 = 8p + 12. \] Now we have: \[ 8p - 3 = 8p + 12. \] Next, let's eliminate the \(8p\) from both sides: \[ -3 = 12. \] Since this is not possible (a contradiction), it means that there are no solutions for \(p\). This indicates that the equation is inconsistent.
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