Question
Solve for \( b \). Give an exact answer. \( 0.75(8 b+4)-1=4 b+14 \)
Ask by Weber Whittaker. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( b=6 \)
Solution
Solve the equation \( 0.75(8b+4)-1=4b+14 \).
Solve the equation by following steps:
- step0: Solve for \(b\):
\(0.75\left(8b+4\right)-1=4b+14\)
- step1: Move the expression to the left side:
\(0.75\left(8b+4\right)-1-\left(4b+14\right)=0\)
- step2: Subtract the terms:
\(0.75\left(8b+4\right)-15-4b=0\)
- step3: Calculate:
\(2b-12=0\)
- step4: Move the constant to the right side:
\(2b=0+12\)
- step5: Remove 0:
\(2b=12\)
- step6: Divide both sides:
\(\frac{2b}{2}=\frac{12}{2}\)
- step7: Divide the numbers:
\(b=6\)
The solution to the equation \(0.75(8b+4)-1=4b+14\) is \(b=6\).
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Simplify this solution The Deep Dive
First, let's simplify the equation step by step. Start by distributing \(0.75\) in the equation: \[ 0.75(8b + 4) - 1 = 4b + 14 \] This simplifies to: \[ 6b + 3 - 1 = 4b + 14 \] Now, combine like terms on the left side: \[ 6b + 2 = 4b + 14 \] Next, isolate \(b\) by subtracting \(4b\) from both sides: \[ 6b - 4b + 2 = 14 \] This simplifies to: \[ 2b + 2 = 14 \] Now, subtract \(2\) from both sides to eliminate the constant: \[ 2b = 12 \] Finally, divide by \(2\): \[ b = 6 \] So, the exact answer for \(b\) is \(6\).
