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The solutions are \( b = -\frac{11}{3} \) and \( b = -1 \).
Solución
Solve the equation \( |2b+6|=|b+5| \).
Solve the equation by following steps:
- step0: Solve for \(b\):
\(\left|2b+6\right|=\left|b+5\right|\)
- step1: Evaluate:
\(\begin{align}&2b+6=b+5\\&2b+6=-\left(b+5\right)\end{align}\)
- step2: Calculate:
\(\begin{align}&b=-1\\&b=-\frac{11}{3}\end{align}\)
- step3: Rewrite:
\(b_{1}=-\frac{11}{3},b_{2}=-1\)
The solution set for the equation \(|2b+6|=|b+5|\) is \(b_{1}=-\frac{11}{3}\) and \(b_{2}=-1\).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To solve the equation \( |2b + 6| = |b + 5| \), we consider two cases based on the properties of absolute values. **Case 1:** \( 2b + 6 = b + 5 \) Solving this, we get: \[ 2b - b + 6 = 5 \] \[ b + 6 = 5 \] \[ b = -1 \] **Case 2:** \( 2b + 6 = - (b + 5) \) Solving this, we get: \[ 2b + 6 = -b - 5 \] \[ 2b + b + 6 + 5 = 0 \] \[ 3b + 11 = 0 \] \[ 3b = -11 \] \[ b = -\frac{11}{3} \] Now we have two solutions: \( b = -1 \) and \( b = -\frac{11}{3} \). Thus, the solution set is: \[ \{ -1, -\frac{11}{3} \} \]
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