Solve the equation:
$3(x-4)+\frac{x+2}{5}=6$
Answer (2)
Multiply both sides of the equation by 5 to eliminate the fraction: 15 ( x − 4 ) + ( x + 2 ) = 30 .
Distribute and combine like terms: 16 x − 58 = 30 .
Add 58 to both sides: 16 x = 88 .
Divide by 16 to find the solution: x = 2 11 .
Explanation
Problem Analysis We are given the equation 3 ( x − 4 ) + 5 x + 2 = 6 and our goal is to solve for x .
Eliminate the Fraction First, we want to eliminate the fraction. To do this, we multiply both sides of the equation by 5: 5 × ( 3 ( x − 4 ) + 5 x + 2 ) = 5 × 6
Distribute the Constant Next, distribute the 5 on the left side of the equation: 5 × 3 ( x − 4 ) + 5 × 5 x + 2 = 30
This simplifies to: 15 ( x − 4 ) + ( x + 2 ) = 30
Distribute Again Now, distribute the 15: 15 x − 60 + x + 2 = 30
Combine Like Terms Combine like terms: 16 x − 58 = 30
Isolate x Term Add 58 to both sides of the equation: 16 x = 30 + 58
16 x = 88
Solve for x Finally, divide both sides by 16 to solve for x : x = 16 88
Simplify the fraction: x = 2 11
x = 5.5
Final Answer Therefore, the solution to the equation is x = 2 11 or x = 5.5 .
Examples
Imagine you're baking a cake and need to adjust a recipe. The recipe calls for a certain amount of flour, but you want to add a bit more and also adjust the amount of sugar to keep the sweetness balanced. Solving equations like this helps you figure out exactly how much more sugar you need to add to maintain the perfect flavor. This kind of problem-solving is useful in cooking, mixing chemicals, or any situation where you need to balance different ingredients or components to achieve a desired outcome.
To solve the equation 3 ( x − 4 ) + 5 x + 2 = 6 , we eliminate the fraction, distribute, combine like terms, isolate the variable, and solve for x , yielding x = 2 11 or 5.5 .
;
