Question
list \( 1 \leftarrow \begin{array}{r}\text { Solve and check the equation } \\ \frac{8 x}{9}=\frac{x}{2}+7 \\ 14\end{array} \)
Ask by Lambert Chadwick. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x=18 \)
Solution
Solve the equation \( \frac{8x}{9}=\frac{x}{2}+7 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{8x}{9}=\frac{x}{2}+7\)
- step1: Multiply both sides of the equation by LCD:
\(\frac{8x}{9}\times 18=\left(\frac{x}{2}+7\right)\times 18\)
- step2: Simplify the equation:
\(16x=9x+126\)
- step3: Move the variable to the left side:
\(16x-9x=126\)
- step4: Subtract the terms:
\(7x=126\)
- step5: Divide both sides:
\(\frac{7x}{7}=\frac{126}{7}\)
- step6: Divide the numbers:
\(x=18\)
The solution to the equation \( \frac{8x}{9}=\frac{x}{2}+7 \) is \( x=18 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve the equation \( \frac{8x}{9} = \frac{x}{2} + 7 \), first eliminate the fractions by finding a common denominator, which is 18. Multiply every term by 18: \[ 18 \cdot \frac{8x}{9} = 18 \cdot \left( \frac{x}{2} + 7 \right) \] This simplifies to: \[ 16x = 9x + 126 \] Now, isolate \( x \) by subtracting \( 9x \) from both sides: \[ 16x - 9x = 126 \] Which gives us: \[ 7x = 126 \] Now, divide by 7: \[ x = 18 \] Finally, checking the answer: Substituting \( x = 18 \) back into the original equation: \[ \frac{8(18)}{9} = \frac{18}{2} + 7 \] This simplifies to: \[ 16 = 9 + 7 \] Since both sides equal 16, the solution checks out! The final answer is: \[ x = 18 \]
