Solve the equation. [tex]9 f-11=3 f+23[/tex]
Answer (2)
Subtract 3 f from both sides: 6 f − 11 = 23 .
Add 11 to both sides: 6 f = 34 .
Divide both sides by 6 : f = 6 34 .
Simplify the fraction: f = 3 17 .
Explanation
Understanding the Problem We are given the equation 9 f − 11 = 3 f + 23 and our goal is to solve for the variable f . This means we want to isolate f on one side of the equation.
Isolating the f term First, let's subtract 3 f from both sides of the equation to get all the f terms on one side: 9 f − 11 − 3 f = 3 f + 23 − 3 f
6 f − 11 = 23
Further isolating f Next, we want to isolate the term with f . To do this, we add 11 to both sides of the equation: 6 f − 11 + 11 = 23 + 11 6 f = 34
Solving for f Finally, to solve for f , we divide both sides of the equation by 6 :
6 6 f = 6 34 f = 6 34 We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: f = 3 17
Final Answer Therefore, the solution to the equation 9 f − 11 = 3 f + 23 is f = 3 17 .
Examples
Imagine you're baking a cake and need to adjust the recipe. If you know that 9 times the amount of flour minus 11 grams should equal 3 times the amount of flour plus 23 grams, solving this equation helps you find the exact amount of flour needed. This type of problem is useful in any situation where you need to balance quantities or find an unknown value based on a given relationship.
To solve the equation 9 f − 11 = 3 f + 23 , we isolate f through a series of steps involving combining like terms and simplifying. The final solution is f = 3 17 . This process illustrates the importance of balancing equations to find unknown variables.
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