$\frac{8 x+4}{5}=\frac{x}{9}$

Multiply both sides by 45 to eliminate fractions: 9 ( 8 x + 4 ) = 5 x .
Distribute and simplify: 72 x + 36 = 5 x .
Combine like terms: 67 x = − 36 .
Solve for x: x = − 67 36 ​ ​ .

Explanation

Problem Setup We are given the equation 5 8 x + 4 ​ = 9 x ​ and we want to solve for x .

Eliminating Fractions To eliminate the fractions, we multiply both sides of the equation by the least common multiple of 5 and 9, which is 45: 45 ⋅ 5 8 x + 4 ​ = 45 ⋅ 9 x ​

Simplification Simplifying both sides, we get: 9 ( 8 x + 4 ) = 5 x

Distribution Distributing the 9 on the left side, we have: 72 x + 36 = 5 x

Isolating x terms Subtracting 5 x from both sides gives: 72 x − 5 x + 36 = 0

Combining Like Terms Simplifying, we get: 67 x + 36 = 0

Isolating x Subtracting 36 from both sides, we have: 67 x = − 36

Solving for x Finally, dividing both sides by 67, we find: x = 67 − 36 ​


Examples
Imagine you're adjusting a recipe that calls for specific ratios of ingredients. If the relationship between two ingredients can be expressed as a linear equation, solving for one variable helps you determine the exact amount needed when you adjust the other. This is crucial in baking or cooking where precise measurements impact the final product. Similarly, in financial planning, if you're trying to balance investments with different growth rates, solving linear equations helps you determine the optimal allocation to achieve your financial goals.

Answered by GinnyAnswer | 2025-07-07

We solved the equation 5 8 x + 4 ​ = 9 x ​ by eliminating fractions and isolating the variable. The solution for x is 67 − 36 ​ . This process demonstrates basic algebraic manipulation techniques.
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Answered by Anonymous | 2025-07-28