Can $3x$ and $-29x$ be combined?
Step 2: Isolate the variable term by adding this value to both sides of the equation: $\square$
$\frac{25}{9} x-\frac{1}{5}=\frac{124}{5}$
Answer (2)
Combine like terms: 3 x + ( − 29 x ) = − 26 x .
Isolate the variable term: 9 25 x = 5 124 + 5 1 .
Simplify the equation: 9 25 x = 25 .
Solve for x : x = 9 . The combined term is − 26 x and the solution to the equation is 9 .
Explanation
Problem Analysis We are given two tasks: first, to combine the like terms 3 x and − 29 x , and second, to solve the equation 9 25 x − 5 1 = 5 124 . Let's tackle these one at a time.
Combining Like Terms To combine the like terms 3 x and − 29 x , we simply add their coefficients: 3 x + ( − 29 x ) = ( 3 − 29 ) x = − 26 x .
Isolating the Variable Term Now, let's solve the equation 9 25 x − 5 1 = 5 124 . To isolate the variable term, we add 5 1 to both sides of the equation: 9 25 x = 5 124 + 5 1 .
Simplifying the Equation Next, we simplify the right side of the equation: 5 124 + 5 1 = 5 125 = 25. So our equation becomes: 9 25 x = 25.
Solving for x To solve for x , we multiply both sides of the equation by 25 9 :
x = 25 ⋅ 25 9 = 9.
Final Answer Therefore, the combined term is − 26 x , and the solution to the equation is x = 9 .
Examples
Imagine you're managing a budget. Combining like terms is like adding up all your income from different sources (salary, investments) and subtracting all your expenses (rent, food, entertainment) to see your net savings. Solving an equation is like figuring out how much you need to save each month to reach a specific financial goal, such as buying a car or a house. These algebraic skills are fundamental to financial planning and decision-making.
The terms 3 x and − 29 x can be combined to form − 26 x . To solve the equation 9 25 x − 5 1 = 5 124 , we isolate x and find that x = 9 .
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