Solve this equation: [tex]3 x-\frac{1}{5}-\frac{2}{9} x=\frac{124}{5}[/tex]
Step 1: Simplify by combining like terms. Which terms can [tex]3 x-\frac{1}{5}-\frac{2}{9} x=\frac{124}{5}[/tex] be combined?
Answer (2)
Combine like terms: 3 x − 9 2 x = 9 25 x .
Move the constant to the right side: 9 25 x = 5 124 + 5 1 = 25 .
Isolate x by multiplying both sides by 25 9 : x = 25 ⋅ 25 9 .
Simplify to find the solution: x = 9 .
Explanation
Identifying Like Terms We are given the equation 3 x − f r a c 1 5 − f r a c 2 9 x = f r a c 124 5 . Our goal is to simplify the equation by combining like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with x : 3 x and − f r a c 2 9 x , and two constant terms: − f r a c 1 5 and f r a c 124 5 .
Combining Like Terms The terms that can be combined are 3 x and − f r a c 2 9 x , which are both terms containing the variable x , and the constants − f r a c 1 5 and f r a c 124 5 .
Solving for x First, let's combine the terms with x : 3 x − f r a c 2 9 x = f r a c 27 9 x − f r a c 2 9 x = f r a c 25 9 x Now, let's move the constant term − f r a c 1 5 to the right side of the equation: f r a c 25 9 x = f r a c 124 5 + f r a c 1 5 Simplify the right side of the equation: f r a c 124 5 + f r a c 1 5 = f r a c 125 5 = 25 Now the equation is: f r a c 25 9 x = 25 Multiply both sides of the equation by f r a c 9 25 to isolate x :
x = 25 c d o t f r a c 9 25 Simplify to find the value of x :
x = 9
Final Answer Therefore, the solution to the equation is x = 9 .
Examples
Imagine you're baking a cake and need to adjust the ingredient quantities. If the original recipe calls for 3 x cups of flour but you decide to reduce it by 9 2 x cups, solving a linear equation helps you determine the exact amount of flour you need. This kind of problem-solving is useful in many real-life situations, from cooking and budgeting to engineering and construction, where precise adjustments are necessary for optimal results.
To solve the equation 3 x − 5 1 − 9 2 x = 5 124 , we first combine like terms to get 9 25 x = 25 and then isolate x to find that x = 9 .
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