Question
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Tutor-Verified Answer
Answer
\( x = \frac{10}{11} \)
Solution
Solve the equation \( \frac{5x+2}{2x+2}=\frac{12}{7} \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{5x+2}{2x+2}=\frac{12}{7}\)
- step1: Find the domain:
\(\frac{5x+2}{2x+2}=\frac{12}{7},x\neq -1\)
- step2: Cross multiply:
\(\left(5x+2\right)\times 7=\left(2x+2\right)\times 12\)
- step3: Simplify the equation:
\(7\left(5x+2\right)=12\left(2x+2\right)\)
- step4: Calculate:
\(35x+14=12\left(2x+2\right)\)
- step5: Calculate:
\(35x+14=24x+24\)
- step6: Move the expression to the left side:
\(35x+14-\left(24x+24\right)=0\)
- step7: Calculate:
\(11x-10=0\)
- step8: Move the constant to the right side:
\(11x=0+10\)
- step9: Remove 0:
\(11x=10\)
- step10: Divide both sides:
\(\frac{11x}{11}=\frac{10}{11}\)
- step11: Divide the numbers:
\(x=\frac{10}{11}\)
- step12: Check if the solution is in the defined range:
\(x=\frac{10}{11},x\neq -1\)
- step13: Find the intersection:
\(x=\frac{10}{11}\)
The solution to the equation \( \frac{5x+2}{2x+2}=\frac{12}{7} \) is \( x = \frac{10}{11} \) or \( x = 0.\dot{9}\dot{0} \).
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Simplify this solution Beyond the Answer
To solve the equation \( \frac{5x + 2}{2x + 2} = \frac{12}{7} \), we can start by cross-multiplying. This gives us: \[ 7(5x + 2) = 12(2x + 2) \] Expanding both sides: \[ 35x + 14 = 24x + 24 \] Now, let's combine like terms by moving \( 24x \) to the left side and \( 14 \) to the right side: \[ 35x - 24x = 24 - 14 \] This simplifies to: \[ 11x = 10 \] Now, divide both sides by \( 11 \): \[ x = \frac{10}{11} \] So, \( x = \frac{10}{11} \).
