Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 0.75 \)
Solution
Solve the equation \( \frac{4x+5}{2x+1}=\frac{16}{5} \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{4x+5}{2x+1}=\frac{16}{5}\)
- step1: Find the domain:
\(\frac{4x+5}{2x+1}=\frac{16}{5},x\neq -\frac{1}{2}\)
- step2: Cross multiply:
\(\left(4x+5\right)\times 5=\left(2x+1\right)\times 16\)
- step3: Simplify the equation:
\(5\left(4x+5\right)=16\left(2x+1\right)\)
- step4: Calculate:
\(20x+25=16\left(2x+1\right)\)
- step5: Calculate:
\(20x+25=32x+16\)
- step6: Move the expression to the left side:
\(20x+25-\left(32x+16\right)=0\)
- step7: Calculate:
\(-12x+9=0\)
- step8: Move the constant to the right side:
\(-12x=0-9\)
- step9: Remove 0:
\(-12x=-9\)
- step10: Change the signs:
\(12x=9\)
- step11: Divide both sides:
\(\frac{12x}{12}=\frac{9}{12}\)
- step12: Divide the numbers:
\(x=\frac{3}{4}\)
- step13: Check if the solution is in the defined range:
\(x=\frac{3}{4},x\neq -\frac{1}{2}\)
- step14: Find the intersection:
\(x=\frac{3}{4}\)
The solution to the equation \( \frac{4x+5}{2x+1}=\frac{16}{5} \) is \( x = \frac{3}{4} \) or \( x = 0.75 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
To solve the equation \(\frac{4x + 5}{2x + 1} = \frac{16}{5}\), you can cross-multiply to eliminate the fractions. This gives you \(5(4x + 5) = 16(2x + 1)\). When you expand both sides, you get \(20x + 25 = 32x + 16\). Rearranging terms leads to \(25 - 16 = 32x - 20x\), which simplifies to \(9 = 12x\). Finally, solving for \(x\) gives you \(x = \frac{3}{4}\). Now that you have your solution, it's always a good idea to check! Substitute \(x = \frac{3}{4}\) back into the original equation to ensure both sides are equal. This is a crucial step to guarantee you haven’t made any errors along the way. Wouldn’t want all that effort to go to waste!
