Question
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Tutor-Verified Answer
Answer
\( b = -1.5 \)
Solution
Solve the equation \( \frac{7}{b+5}=\frac{10}{5} \).
Solve the equation by following steps:
- step0: Solve for \(b\):
\(\frac{7}{b+5}=\frac{10}{5}\)
- step1: Find the domain:
\(\frac{7}{b+5}=\frac{10}{5},b\neq -5\)
- step2: Divide the terms:
\(\frac{7}{b+5}=2\)
- step3: Cross multiply:
\(7=\left(b+5\right)\times 2\)
- step4: Simplify the equation:
\(7=2\left(b+5\right)\)
- step5: Swap the sides:
\(2\left(b+5\right)=7\)
- step6: Divide both sides:
\(\frac{2\left(b+5\right)}{2}=\frac{7}{2}\)
- step7: Divide the numbers:
\(b+5=\frac{7}{2}\)
- step8: Move the constant to the right side:
\(b=\frac{7}{2}-5\)
- step9: Subtract the numbers:
\(b=-\frac{3}{2}\)
- step10: Check if the solution is in the defined range:
\(b=-\frac{3}{2},b\neq -5\)
- step11: Find the intersection:
\(b=-\frac{3}{2}\)
The solution to the equation \( \frac{7}{b+5}=\frac{10}{5} \) is \( b = -\frac{3}{2} \) or \( b = -1.5 \).
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Simplify this solution The Deep Dive
To solve the equation \( \frac{7}{b+5}=\frac{10}{5} \), first simplify the right side. Since \( \frac{10}{5} = 2 \), the equation becomes \( \frac{7}{b+5} = 2 \). To eliminate the fraction, multiply both sides by \( b + 5 \), giving you \( 7 = 2(b + 5) \). Expanding the right side results in \( 7 = 2b + 10 \). Now, subtract 10 from both sides: \( 7 - 10 = 2b \) or \( -3 = 2b \). Finally, divide by 2 to find \( b = -\frac{3}{2} \) or \( b = -1.5 \). And voilà! You have your value for \( b \).
